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

Percentage Accurate: 85.2% → 91.6%

Time: 12.3s

Alternatives: 14

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% 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: 91.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 50.7%

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

      1. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in y around inf 99.7%

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

   7. Simplified 99.7%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2.0000000000000001e270

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

      1. sub-neg 94.9%

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

      2. +-commutative 94.9%

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

      3. distribute-lft-neg-in 94.9%

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

      4. fma-define 95.0%

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

   6. Applied egg-rr 95.0%

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

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

   1. Initial program 43.3%

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

      1. *-commutative 43.3%

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

   3. Simplified 43.3%

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

   5. Taylor expanded in x around inf 43.3%

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

      1. mul-1-neg 43.3%

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

      2. unsub-neg 43.3%

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

      3. associate-/l* 43.3%

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

   7. Simplified 43.3%

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

   8. Taylor expanded in t around 0 32.9%

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

      1. associate-*r/ 32.9%

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

      2. associate-*r* 32.9%

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

      3. mul-1-neg 32.9%

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

      4. associate-*r/ 32.9%

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

      5. *-commutative 32.9%

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

   10. Simplified 32.9%

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

   11. Taylor expanded in x around 0 89.7%

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

4. Final simplification 94.7%

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

Alternative 2: 91.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 50.7%

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

      1. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in y around inf 99.7%

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

   7. Simplified 99.7%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2.0000000000000001e270

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

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

   1. Initial program 43.3%

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

      1. *-commutative 43.3%

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

   3. Simplified 43.3%

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

   5. Taylor expanded in x around inf 43.3%

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

      1. mul-1-neg 43.3%

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

      2. unsub-neg 43.3%

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

      3. associate-/l* 43.3%

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

   7. Simplified 43.3%

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

   8. Taylor expanded in t around 0 32.9%

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

      1. associate-*r/ 32.9%

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

      2. associate-*r* 32.9%

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

      3. mul-1-neg 32.9%

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

      4. associate-*r/ 32.9%

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

      5. *-commutative 32.9%

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

   10. Simplified 32.9%

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

   11. Taylor expanded in x around 0 89.7%

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

4. Final simplification 94.7%

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

Alternative 3: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ z (- (* z a) t)))
     (if (<= t_1 2e+270) t_1 (- (/ y a) (/ 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 / ((z * a) - t));
	} else if (t_1 <= 2e+270) {
		tmp = t_1;
	} else {
		tmp = (y / a) - (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 / ((z * a) - t));
	} else if (t_1 <= 2e+270) {
		tmp = t_1;
	} else {
		tmp = (y / a) - (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 / ((z * a) - t))
	elif t_1 <= 2e+270:
		tmp = t_1
	else:
		tmp = (y / a) - (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(z / Float64(Float64(z * a) - t)));
	elseif (t_1 <= 2e+270)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) - Float64(x / Float64(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 / ((z * a) - t));
	elseif (t_1 <= 2e+270)
		tmp = t_1;
	else
		tmp = (y / a) - (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[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+270], t$95$1, N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 50.7%

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

      1. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. associate-/l* 84.2%

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

      3. distribute-rgt-neg-in 84.2%

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

      4. distribute-neg-frac2 84.2%

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

      5. cancel-sign-sub-inv 84.2%

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

      6. *-commutative 84.2%

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

      7. +-commutative 84.2%

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

      8. distribute-rgt-neg-out 84.2%

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

      9. distribute-lft-neg-in 84.2%

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

      10. *-commutative 84.2%

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

      11. fma-undefine 84.2%

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

      12. neg-sub0 84.2%

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

      13. fma-undefine 84.2%

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

      14. distribute-rgt-neg-in 84.2%

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

      15. mul-1-neg 84.2%

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

      16. associate-*r* 84.2%

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

      17. neg-mul-1 84.2%

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

      18. *-commutative 84.2%

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

      19. associate--r+ 84.2%

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

      20. neg-sub0 84.2%

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

      21. distribute-rgt-neg-out 84.2%

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

      22. remove-double-neg 84.2%

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

   7. Simplified 84.2%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2.0000000000000001e270

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

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

   1. Initial program 43.3%

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

      1. *-commutative 43.3%

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

   3. Simplified 43.3%

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

   5. Taylor expanded in x around inf 43.3%

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

      1. mul-1-neg 43.3%

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

      2. unsub-neg 43.3%

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

      3. associate-/l* 43.3%

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

   7. Simplified 43.3%

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

   8. Taylor expanded in t around 0 32.9%

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

      1. associate-*r/ 32.9%

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

      2. associate-*r* 32.9%

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

      3. mul-1-neg 32.9%

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

      4. associate-*r/ 32.9%

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

      5. *-commutative 32.9%

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

   10. Simplified 32.9%

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

   11. Taylor expanded in x around 0 89.7%

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

4. Final simplification 93.5%

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

Alternative 4: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+96)
   (/ y a)
   (if (<= z -9.5e+39)
     (* y (/ z (- t)))
     (if (<= z -3.3e-31)
       (* y (/ 1.0 a))
       (if (<= z 1.3e-13)
         (/ x t)
         (if (<= z 1.52e+41)
           (/ (/ (- x) a) z)
           (if (<= z 1.02e+62) (/ (* y z) (- t)) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+96) {
		tmp = y / a;
	} else if (z <= -9.5e+39) {
		tmp = y * (z / -t);
	} else if (z <= -3.3e-31) {
		tmp = y * (1.0 / a);
	} else if (z <= 1.3e-13) {
		tmp = x / t;
	} else if (z <= 1.52e+41) {
		tmp = (-x / a) / z;
	} else if (z <= 1.02e+62) {
		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 <= (-3.8d+96)) then
        tmp = y / a
    else if (z <= (-9.5d+39)) then
        tmp = y * (z / -t)
    else if (z <= (-3.3d-31)) then
        tmp = y * (1.0d0 / a)
    else if (z <= 1.3d-13) then
        tmp = x / t
    else if (z <= 1.52d+41) then
        tmp = (-x / a) / z
    else if (z <= 1.02d+62) 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 <= -3.8e+96) {
		tmp = y / a;
	} else if (z <= -9.5e+39) {
		tmp = y * (z / -t);
	} else if (z <= -3.3e-31) {
		tmp = y * (1.0 / a);
	} else if (z <= 1.3e-13) {
		tmp = x / t;
	} else if (z <= 1.52e+41) {
		tmp = (-x / a) / z;
	} else if (z <= 1.02e+62) {
		tmp = (y * z) / -t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+96:
		tmp = y / a
	elif z <= -9.5e+39:
		tmp = y * (z / -t)
	elif z <= -3.3e-31:
		tmp = y * (1.0 / a)
	elif z <= 1.3e-13:
		tmp = x / t
	elif z <= 1.52e+41:
		tmp = (-x / a) / z
	elif z <= 1.02e+62:
		tmp = (y * z) / -t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+96)
		tmp = Float64(y / a);
	elseif (z <= -9.5e+39)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -3.3e-31)
		tmp = Float64(y * Float64(1.0 / a));
	elseif (z <= 1.3e-13)
		tmp = Float64(x / t);
	elseif (z <= 1.52e+41)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 1.02e+62)
		tmp = Float64(Float64(y * z) / Float64(-t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+96)
		tmp = y / a;
	elseif (z <= -9.5e+39)
		tmp = y * (z / -t);
	elseif (z <= -3.3e-31)
		tmp = y * (1.0 / a);
	elseif (z <= 1.3e-13)
		tmp = x / t;
	elseif (z <= 1.52e+41)
		tmp = (-x / a) / z;
	elseif (z <= 1.02e+62)
		tmp = (y * z) / -t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+96], N[(y / a), $MachinePrecision], If[LessEqual[z, -9.5e+39], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-31], N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-13], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.52e+41], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.02e+62], N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.8000000000000002e96 or 1.02000000000000002e62 < z

   1. Initial program 64.3%

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

      1. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in z around inf 68.2%

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

   if -3.8000000000000002e96 < z < -9.50000000000000011e39

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in t around inf 51.5%

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

      1. associate-/l* 51.5%

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

      2. associate-*r/ 61.1%

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

   10. Simplified 61.1%

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

   11. Taylor expanded in x around 0 51.6%

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

       1. mul-1-neg 51.6%

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

       2. associate-/l* 61.1%

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

       3. distribute-lft-neg-in 61.1%

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

   13. Simplified 61.1%

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

   if -9.50000000000000011e39 < z < -3.2999999999999999e-31

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-/l* 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. distribute-neg-frac2 51.4%

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

      5. cancel-sign-sub-inv 51.4%

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

      6. *-commutative 51.4%

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

      7. +-commutative 51.4%

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

      8. distribute-rgt-neg-out 51.4%

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

      9. distribute-lft-neg-in 51.4%

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

      10. *-commutative 51.4%

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

      11. fma-undefine 51.4%

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

      12. neg-sub0 51.4%

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

      13. fma-undefine 51.4%

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

      14. distribute-rgt-neg-in 51.4%

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

      15. mul-1-neg 51.4%

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

      16. associate-*r* 51.4%

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

      17. neg-mul-1 51.4%

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

      18. *-commutative 51.4%

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

      19. associate--r+ 51.4%

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

      20. neg-sub0 51.4%

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

      21. distribute-rgt-neg-out 51.4%

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

      22. remove-double-neg 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in z around inf 43.7%

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

   if -3.2999999999999999e-31 < z < 1.3e-13

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 59.9%

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

   if 1.3e-13 < z < 1.52000000000000002e41

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. associate-/r* 55.0%

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

      3. distribute-neg-frac 55.0%

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

      4. distribute-neg-frac2 55.0%

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

   10. Simplified 55.0%

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

   if 1.52000000000000002e41 < z < 1.02000000000000002e62

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. associate-/l* 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

      4. distribute-neg-frac2 64.6%

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

      5. cancel-sign-sub-inv 64.6%

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

      6. *-commutative 64.6%

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

      7. +-commutative 64.6%

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

      8. distribute-rgt-neg-out 64.6%

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

      9. distribute-lft-neg-in 64.6%

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

      10. *-commutative 64.6%

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

      11. fma-undefine 64.6%

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

      12. neg-sub0 64.6%

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

      13. fma-undefine 64.6%

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

      14. distribute-rgt-neg-in 64.6%

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

      15. mul-1-neg 64.6%

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

      16. associate-*r* 64.6%

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

      17. neg-mul-1 64.6%

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

      18. *-commutative 64.6%

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

      19. associate--r+ 64.6%

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

      20. neg-sub0 64.6%

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

      21. distribute-rgt-neg-out 64.6%

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

      22. remove-double-neg 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around 0 65.0%

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

      1. associate-*r/ 65.0%

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

      2. associate-*r* 65.0%

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

      3. mul-1-neg 65.0%

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

   10. Simplified 65.0%

       \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot z}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+101)
   (/ y a)
   (if (<= z -1.5e+40)
     (* y (/ z (- t)))
     (if (<= z -2.3e-30)
       (* y (/ 1.0 a))
       (if (<= z 3.6e-13)
         (/ x t)
         (if (<= z 4.2e+50)
           (/ x (* z (- a)))
           (if (<= z 1.02e+62) (/ (* y z) (- t)) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+101) {
		tmp = y / a;
	} else if (z <= -1.5e+40) {
		tmp = y * (z / -t);
	} else if (z <= -2.3e-30) {
		tmp = y * (1.0 / a);
	} else if (z <= 3.6e-13) {
		tmp = x / t;
	} else if (z <= 4.2e+50) {
		tmp = x / (z * -a);
	} else if (z <= 1.02e+62) {
		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 <= (-2.4d+101)) then
        tmp = y / a
    else if (z <= (-1.5d+40)) then
        tmp = y * (z / -t)
    else if (z <= (-2.3d-30)) then
        tmp = y * (1.0d0 / a)
    else if (z <= 3.6d-13) then
        tmp = x / t
    else if (z <= 4.2d+50) then
        tmp = x / (z * -a)
    else if (z <= 1.02d+62) 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 <= -2.4e+101) {
		tmp = y / a;
	} else if (z <= -1.5e+40) {
		tmp = y * (z / -t);
	} else if (z <= -2.3e-30) {
		tmp = y * (1.0 / a);
	} else if (z <= 3.6e-13) {
		tmp = x / t;
	} else if (z <= 4.2e+50) {
		tmp = x / (z * -a);
	} else if (z <= 1.02e+62) {
		tmp = (y * z) / -t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+101:
		tmp = y / a
	elif z <= -1.5e+40:
		tmp = y * (z / -t)
	elif z <= -2.3e-30:
		tmp = y * (1.0 / a)
	elif z <= 3.6e-13:
		tmp = x / t
	elif z <= 4.2e+50:
		tmp = x / (z * -a)
	elif z <= 1.02e+62:
		tmp = (y * z) / -t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+101)
		tmp = Float64(y / a);
	elseif (z <= -1.5e+40)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -2.3e-30)
		tmp = Float64(y * Float64(1.0 / a));
	elseif (z <= 3.6e-13)
		tmp = Float64(x / t);
	elseif (z <= 4.2e+50)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 1.02e+62)
		tmp = Float64(Float64(y * z) / Float64(-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 <= -2.4e+101)
		tmp = y / a;
	elseif (z <= -1.5e+40)
		tmp = y * (z / -t);
	elseif (z <= -2.3e-30)
		tmp = y * (1.0 / a);
	elseif (z <= 3.6e-13)
		tmp = x / t;
	elseif (z <= 4.2e+50)
		tmp = x / (z * -a);
	elseif (z <= 1.02e+62)
		tmp = (y * z) / -t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+101], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.5e+40], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-30], N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-13], N[(x / t), $MachinePrecision], If[LessEqual[z, 4.2e+50], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+62], N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.39999999999999988e101 or 1.02000000000000002e62 < z

   1. Initial program 64.3%

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

      1. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in z around inf 68.2%

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

   if -2.39999999999999988e101 < z < -1.5000000000000001e40

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in t around inf 51.5%

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

      1. associate-/l* 51.5%

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

      2. associate-*r/ 61.1%

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

   10. Simplified 61.1%

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

   11. Taylor expanded in x around 0 51.6%

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

       1. mul-1-neg 51.6%

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

       2. associate-/l* 61.1%

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

       3. distribute-lft-neg-in 61.1%

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

   13. Simplified 61.1%

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

   if -1.5000000000000001e40 < z < -2.29999999999999984e-30

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-/l* 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. distribute-neg-frac2 51.4%

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

      5. cancel-sign-sub-inv 51.4%

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

      6. *-commutative 51.4%

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

      7. +-commutative 51.4%

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

      8. distribute-rgt-neg-out 51.4%

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

      9. distribute-lft-neg-in 51.4%

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

      10. *-commutative 51.4%

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

      11. fma-undefine 51.4%

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

      12. neg-sub0 51.4%

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

      13. fma-undefine 51.4%

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

      14. distribute-rgt-neg-in 51.4%

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

      15. mul-1-neg 51.4%

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

      16. associate-*r* 51.4%

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

      17. neg-mul-1 51.4%

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

      18. *-commutative 51.4%

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

      19. associate--r+ 51.4%

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

      20. neg-sub0 51.4%

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

      21. distribute-rgt-neg-out 51.4%

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

      22. remove-double-neg 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in z around inf 43.7%

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

   if -2.29999999999999984e-30 < z < 3.5999999999999998e-13

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 59.9%

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

   if 3.5999999999999998e-13 < z < 4.1999999999999999e50

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 54.9%

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

      1. associate-*r/ 54.9%

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

      2. mul-1-neg 54.9%

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

      3. *-commutative 54.9%

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

   10. Simplified 54.9%

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

   if 4.1999999999999999e50 < z < 1.02000000000000002e62

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. associate-/l* 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

      4. distribute-neg-frac2 64.6%

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

      5. cancel-sign-sub-inv 64.6%

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

      6. *-commutative 64.6%

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

      7. +-commutative 64.6%

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

      8. distribute-rgt-neg-out 64.6%

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

      9. distribute-lft-neg-in 64.6%

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

      10. *-commutative 64.6%

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

      11. fma-undefine 64.6%

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

      12. neg-sub0 64.6%

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

      13. fma-undefine 64.6%

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

      14. distribute-rgt-neg-in 64.6%

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

      15. mul-1-neg 64.6%

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

      16. associate-*r* 64.6%

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

      17. neg-mul-1 64.6%

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

      18. *-commutative 64.6%

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

      19. associate--r+ 64.6%

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

      20. neg-sub0 64.6%

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

      21. distribute-rgt-neg-out 64.6%

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

      22. remove-double-neg 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around 0 65.0%

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

      1. associate-*r/ 65.0%

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

      2. associate-*r* 65.0%

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

      3. mul-1-neg 65.0%

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

   10. Simplified 65.0%

       \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot z}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-t}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t)))))
   (if (<= z -3.9e+96)
     (/ y a)
     (if (<= z -2.15e+42)
       t_1
       (if (<= z -2.3e-30)
         (* y (/ 1.0 a))
         (if (<= z 1.02e-13)
           (/ x t)
           (if (<= z 3e+34)
             (/ x (* z (- a)))
             (if (<= z 1e+62) t_1 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -t);
	double tmp;
	if (z <= -3.9e+96) {
		tmp = y / a;
	} else if (z <= -2.15e+42) {
		tmp = t_1;
	} else if (z <= -2.3e-30) {
		tmp = y * (1.0 / a);
	} else if (z <= 1.02e-13) {
		tmp = x / t;
	} else if (z <= 3e+34) {
		tmp = x / (z * -a);
	} else if (z <= 1e+62) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / -t)
    if (z <= (-3.9d+96)) then
        tmp = y / a
    else if (z <= (-2.15d+42)) then
        tmp = t_1
    else if (z <= (-2.3d-30)) then
        tmp = y * (1.0d0 / a)
    else if (z <= 1.02d-13) then
        tmp = x / t
    else if (z <= 3d+34) then
        tmp = x / (z * -a)
    else if (z <= 1d+62) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -t);
	double tmp;
	if (z <= -3.9e+96) {
		tmp = y / a;
	} else if (z <= -2.15e+42) {
		tmp = t_1;
	} else if (z <= -2.3e-30) {
		tmp = y * (1.0 / a);
	} else if (z <= 1.02e-13) {
		tmp = x / t;
	} else if (z <= 3e+34) {
		tmp = x / (z * -a);
	} else if (z <= 1e+62) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -t)
	tmp = 0
	if z <= -3.9e+96:
		tmp = y / a
	elif z <= -2.15e+42:
		tmp = t_1
	elif z <= -2.3e-30:
		tmp = y * (1.0 / a)
	elif z <= 1.02e-13:
		tmp = x / t
	elif z <= 3e+34:
		tmp = x / (z * -a)
	elif z <= 1e+62:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(-t)))
	tmp = 0.0
	if (z <= -3.9e+96)
		tmp = Float64(y / a);
	elseif (z <= -2.15e+42)
		tmp = t_1;
	elseif (z <= -2.3e-30)
		tmp = Float64(y * Float64(1.0 / a));
	elseif (z <= 1.02e-13)
		tmp = Float64(x / t);
	elseif (z <= 3e+34)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 1e+62)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / -t);
	tmp = 0.0;
	if (z <= -3.9e+96)
		tmp = y / a;
	elseif (z <= -2.15e+42)
		tmp = t_1;
	elseif (z <= -2.3e-30)
		tmp = y * (1.0 / a);
	elseif (z <= 1.02e-13)
		tmp = x / t;
	elseif (z <= 3e+34)
		tmp = x / (z * -a);
	elseif (z <= 1e+62)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+96], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.15e+42], t$95$1, If[LessEqual[z, -2.3e-30], N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-13], N[(x / t), $MachinePrecision], If[LessEqual[z, 3e+34], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+62], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.9e96 or 1.00000000000000004e62 < z

   1. Initial program 64.3%

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

      1. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in z around inf 68.2%

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

   if -3.9e96 < z < -2.1499999999999999e42 or 3.00000000000000018e34 < z < 1.00000000000000004e62

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

      3. associate-/l* 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in t around inf 65.3%

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

      1. associate-/l* 65.1%

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

      2. associate-*r/ 72.1%

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

   10. Simplified 72.1%

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

   11. Taylor expanded in x around 0 55.4%

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

       1. mul-1-neg 55.4%

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

       2. associate-/l* 62.1%

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

       3. distribute-lft-neg-in 62.1%

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

   13. Simplified 62.1%

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

   if -2.1499999999999999e42 < z < -2.29999999999999984e-30

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-/l* 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. distribute-neg-frac2 51.4%

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

      5. cancel-sign-sub-inv 51.4%

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

      6. *-commutative 51.4%

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

      7. +-commutative 51.4%

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

      8. distribute-rgt-neg-out 51.4%

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

      9. distribute-lft-neg-in 51.4%

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

      10. *-commutative 51.4%

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

      11. fma-undefine 51.4%

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

      12. neg-sub0 51.4%

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

      13. fma-undefine 51.4%

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

      14. distribute-rgt-neg-in 51.4%

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

      15. mul-1-neg 51.4%

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

      16. associate-*r* 51.4%

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

      17. neg-mul-1 51.4%

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

      18. *-commutative 51.4%

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

      19. associate--r+ 51.4%

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

      20. neg-sub0 51.4%

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

      21. distribute-rgt-neg-out 51.4%

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

      22. remove-double-neg 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in z around inf 43.7%

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

   if -2.29999999999999984e-30 < z < 1.0199999999999999e-13

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 59.9%

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

   if 1.0199999999999999e-13 < z < 3.00000000000000018e34

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 60.7%

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

      1. *-commutative 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 54.9%

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

      1. associate-*r/ 54.9%

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

      2. mul-1-neg 54.9%

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

      3. *-commutative 54.9%

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

   10. Simplified 54.9%

       \[\leadsto \color{blue}{\frac{-x}{z \cdot a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 10^{+62}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+61} \lor \neg \left(t \leq -2 \cdot 10^{+23} \lor \neg \left(t \leq -1.7 \cdot 10^{-39}\right) \land t \leq 2.2 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+61)
         (not (or (<= t -2e+23) (and (not (<= t -1.7e-39)) (<= t 2.2e+33)))))
   (- (/ x t) (* z (/ y t)))
   (- (/ y a) (/ x (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+61) || !((t <= -2e+23) || (!(t <= -1.7e-39) && (t <= 2.2e+33)))) {
		tmp = (x / t) - (z * (y / t));
	} else {
		tmp = (y / a) - (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) :: tmp
    if ((t <= (-8.5d+61)) .or. (.not. (t <= (-2d+23)) .or. (.not. (t <= (-1.7d-39))) .and. (t <= 2.2d+33))) then
        tmp = (x / t) - (z * (y / t))
    else
        tmp = (y / a) - (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 tmp;
	if ((t <= -8.5e+61) || !((t <= -2e+23) || (!(t <= -1.7e-39) && (t <= 2.2e+33)))) {
		tmp = (x / t) - (z * (y / t));
	} else {
		tmp = (y / a) - (x / (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+61) or not ((t <= -2e+23) or (not (t <= -1.7e-39) and (t <= 2.2e+33))):
		tmp = (x / t) - (z * (y / t))
	else:
		tmp = (y / a) - (x / (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+61) || !((t <= -2e+23) || (!(t <= -1.7e-39) && (t <= 2.2e+33))))
		tmp = Float64(Float64(x / t) - Float64(z * Float64(y / t)));
	else
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e+61) || ~(((t <= -2e+23) || (~((t <= -1.7e-39)) && (t <= 2.2e+33)))))
		tmp = (x / t) - (z * (y / t));
	else
		tmp = (y / a) - (x / (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+61], N[Not[Or[LessEqual[t, -2e+23], And[N[Not[LessEqual[t, -1.7e-39]], $MachinePrecision], LessEqual[t, 2.2e+33]]]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000035e61 or -1.9999999999999998e23 < t < -1.7e-39 or 2.19999999999999994e33 < t

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around 0 70.6%

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

   6. Taylor expanded in y around inf 76.0%

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

      1. neg-mul-1 76.0%

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

      2. distribute-neg-frac 76.0%

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

   8. Simplified 76.0%

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

   if -8.50000000000000035e61 < t < -1.9999999999999998e23 or -1.7e-39 < t < 2.19999999999999994e33

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

      3. associate-/l* 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in t around 0 61.2%

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

      1. associate-*r/ 61.2%

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

      2. associate-*r* 61.2%

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

      3. mul-1-neg 61.2%

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

      4. associate-*r/ 59.7%

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

      5. *-commutative 59.7%

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

   10. Simplified 59.7%

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

   11. Taylor expanded in x around 0 78.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+61} \lor \neg \left(t \leq -2 \cdot 10^{+23} \lor \neg \left(t \leq -1.7 \cdot 10^{-39}\right) \land t \leq 2.2 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 650:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+100)
   (/ y a)
   (if (<= z -6e+41)
     (* y (/ z (- t)))
     (if (<= z -2.9e-30) (* y (/ 1.0 a)) (if (<= z 650.0) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+100) {
		tmp = y / a;
	} else if (z <= -6e+41) {
		tmp = y * (z / -t);
	} else if (z <= -2.9e-30) {
		tmp = y * (1.0 / a);
	} else if (z <= 650.0) {
		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 <= (-6.8d+100)) then
        tmp = y / a
    else if (z <= (-6d+41)) then
        tmp = y * (z / -t)
    else if (z <= (-2.9d-30)) then
        tmp = y * (1.0d0 / a)
    else if (z <= 650.0d0) 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 <= -6.8e+100) {
		tmp = y / a;
	} else if (z <= -6e+41) {
		tmp = y * (z / -t);
	} else if (z <= -2.9e-30) {
		tmp = y * (1.0 / a);
	} else if (z <= 650.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+100:
		tmp = y / a
	elif z <= -6e+41:
		tmp = y * (z / -t)
	elif z <= -2.9e-30:
		tmp = y * (1.0 / a)
	elif z <= 650.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+100)
		tmp = Float64(y / a);
	elseif (z <= -6e+41)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -2.9e-30)
		tmp = Float64(y * Float64(1.0 / a));
	elseif (z <= 650.0)
		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 <= -6.8e+100)
		tmp = y / a;
	elseif (z <= -6e+41)
		tmp = y * (z / -t);
	elseif (z <= -2.9e-30)
		tmp = y * (1.0 / a);
	elseif (z <= 650.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+100], N[(y / a), $MachinePrecision], If[LessEqual[z, -6e+41], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-30], N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 650.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999988e100 or 650 < z

   1. Initial program 69.3%

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

      1. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in z around inf 62.6%

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

   if -6.79999999999999988e100 < z < -5.9999999999999997e41

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in t around inf 51.5%

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

      1. associate-/l* 51.5%

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

      2. associate-*r/ 61.1%

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

   10. Simplified 61.1%

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

   11. Taylor expanded in x around 0 51.6%

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

       1. mul-1-neg 51.6%

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

       2. associate-/l* 61.1%

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

       3. distribute-lft-neg-in 61.1%

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

   13. Simplified 61.1%

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

   if -5.9999999999999997e41 < z < -2.89999999999999989e-30

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-/l* 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. distribute-neg-frac2 51.4%

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

      5. cancel-sign-sub-inv 51.4%

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

      6. *-commutative 51.4%

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

      7. +-commutative 51.4%

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

      8. distribute-rgt-neg-out 51.4%

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

      9. distribute-lft-neg-in 51.4%

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

      10. *-commutative 51.4%

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

      11. fma-undefine 51.4%

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

      12. neg-sub0 51.4%

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

      13. fma-undefine 51.4%

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

      14. distribute-rgt-neg-in 51.4%

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

      15. mul-1-neg 51.4%

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

      16. associate-*r* 51.4%

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

      17. neg-mul-1 51.4%

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

      18. *-commutative 51.4%

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

      19. associate--r+ 51.4%

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

      20. neg-sub0 51.4%

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

      21. distribute-rgt-neg-out 51.4%

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

      22. remove-double-neg 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in z around inf 43.7%

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

   if -2.89999999999999989e-30 < z < 650

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 58.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 650:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 1350:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+100)
   (/ y a)
   (if (<= z -5.6e+41)
     (* y (/ z (- t)))
     (if (<= z -1.85e-31)
       (* y (/ 1.0 a))
       (if (<= z 1350.0) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+100) {
		tmp = y / a;
	} else if (z <= -5.6e+41) {
		tmp = y * (z / -t);
	} else if (z <= -1.85e-31) {
		tmp = y * (1.0 / a);
	} else if (z <= 1350.0) {
		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 <= (-6.8d+100)) then
        tmp = y / a
    else if (z <= (-5.6d+41)) then
        tmp = y * (z / -t)
    else if (z <= (-1.85d-31)) then
        tmp = y * (1.0d0 / a)
    else if (z <= 1350.0d0) 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 <= -6.8e+100) {
		tmp = y / a;
	} else if (z <= -5.6e+41) {
		tmp = y * (z / -t);
	} else if (z <= -1.85e-31) {
		tmp = y * (1.0 / a);
	} else if (z <= 1350.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+100:
		tmp = y / a
	elif z <= -5.6e+41:
		tmp = y * (z / -t)
	elif z <= -1.85e-31:
		tmp = y * (1.0 / a)
	elif z <= 1350.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+100)
		tmp = Float64(y / a);
	elseif (z <= -5.6e+41)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -1.85e-31)
		tmp = Float64(y * Float64(1.0 / a));
	elseif (z <= 1350.0)
		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 <= -6.8e+100)
		tmp = y / a;
	elseif (z <= -5.6e+41)
		tmp = y * (z / -t);
	elseif (z <= -1.85e-31)
		tmp = y * (1.0 / a);
	elseif (z <= 1350.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+100], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.6e+41], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-31], N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1350.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999988e100 or 1350 < z

   1. Initial program 69.3%

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

      1. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in z around inf 62.6%

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

   if -6.79999999999999988e100 < z < -5.5999999999999999e41

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 61.3%

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

      3. distribute-rgt-neg-in 61.3%

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

      4. distribute-neg-frac2 61.3%

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

      5. cancel-sign-sub-inv 61.3%

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

      6. *-commutative 61.3%

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

      7. +-commutative 61.3%

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

      8. distribute-rgt-neg-out 61.3%

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

      9. distribute-lft-neg-in 61.3%

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

      10. *-commutative 61.3%

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

      11. fma-undefine 61.3%

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

      12. neg-sub0 61.3%

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

      13. fma-undefine 61.3%

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

      14. distribute-rgt-neg-in 61.3%

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

      15. mul-1-neg 61.3%

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

      16. associate-*r* 61.3%

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

      17. neg-mul-1 61.3%

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

      18. *-commutative 61.3%

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

      19. associate--r+ 61.3%

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

      20. neg-sub0 61.3%

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

      21. distribute-rgt-neg-out 61.3%

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

      22. remove-double-neg 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in z around 0 61.1%

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

      1. associate-*r/ 61.1%

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

      2. neg-mul-1 61.1%

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

   10. Simplified 61.1%

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

   if -5.5999999999999999e41 < z < -1.8499999999999999e-31

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-/l* 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. distribute-neg-frac2 51.4%

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

      5. cancel-sign-sub-inv 51.4%

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

      6. *-commutative 51.4%

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

      7. +-commutative 51.4%

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

      8. distribute-rgt-neg-out 51.4%

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

      9. distribute-lft-neg-in 51.4%

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

      10. *-commutative 51.4%

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

      11. fma-undefine 51.4%

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

      12. neg-sub0 51.4%

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

      13. fma-undefine 51.4%

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

      14. distribute-rgt-neg-in 51.4%

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

      15. mul-1-neg 51.4%

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

      16. associate-*r* 51.4%

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

      17. neg-mul-1 51.4%

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

      18. *-commutative 51.4%

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

      19. associate--r+ 51.4%

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

      20. neg-sub0 51.4%

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

      21. distribute-rgt-neg-out 51.4%

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

      22. remove-double-neg 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in z around inf 43.7%

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

   if -1.8499999999999999e-31 < z < 1350

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 58.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{1}{a}\\ \mathbf{elif}\;z \leq 1350:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+102} \lor \neg \left(y \leq 1.35 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.3e+102) (not (<= y 1.35e+45)))
   (* y (/ z (- (* z a) t)))
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.3e+102) || !(y <= 1.35e+45)) {
		tmp = y * (z / ((z * a) - t));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.3d+102)) .or. (.not. (y <= 1.35d+45))) then
        tmp = y * (z / ((z * a) - t))
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.3e+102) || !(y <= 1.35e+45)) {
		tmp = y * (z / ((z * a) - t));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.3e+102) or not (y <= 1.35e+45):
		tmp = y * (z / ((z * a) - t))
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.3e+102) || !(y <= 1.35e+45))
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.3e+102) || ~((y <= 1.35e+45)))
		tmp = y * (z / ((z * a) - t));
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.3e+102], N[Not[LessEqual[y, 1.35e+45]], $MachinePrecision]], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999999e102 or 1.34999999999999992e45 < y

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in x around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-/l* 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

      4. distribute-neg-frac2 72.1%

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

      5. cancel-sign-sub-inv 72.1%

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

      6. *-commutative 72.1%

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

      7. +-commutative 72.1%

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

      8. distribute-rgt-neg-out 72.1%

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

      9. distribute-lft-neg-in 72.1%

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

      10. *-commutative 72.1%

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

      11. fma-undefine 72.1%

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

      12. neg-sub0 72.1%

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

      13. fma-undefine 72.1%

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

      14. distribute-rgt-neg-in 72.1%

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

      15. mul-1-neg 72.1%

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

      16. associate-*r* 72.1%

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

      17. neg-mul-1 72.1%

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

      18. *-commutative 72.1%

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

      19. associate--r+ 72.1%

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

      20. neg-sub0 72.1%

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

      21. distribute-rgt-neg-out 72.1%

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

      22. remove-double-neg 72.1%

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

   7. Simplified 72.1%

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

   if -2.2999999999999999e102 < y < 1.34999999999999992e45

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

   7. Simplified 71.7%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+102} \lor \neg \left(y \leq 1.35 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+105} \lor \neg \left(z \leq 2.55 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+105) (not (<= z 2.55e+67))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+105) || !(z <= 2.55e+67)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.2d+105)) .or. (.not. (z <= 2.55d+67))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+105) || !(z <= 2.55e+67)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+105) or not (z <= 2.55e+67):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+105) || !(z <= 2.55e+67))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e+105) || ~((z <= 2.55e+67)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+105], N[Not[LessEqual[z, 2.55e+67]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e105 or 2.5500000000000001e67 < z

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in z around inf 69.2%

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

   if -3.2e105 < z < 2.5500000000000001e67

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 67.3%

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

      1. *-commutative 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+105} \lor \neg \left(z \leq 2.55 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+108}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -8.4e+108)
   (/ y a)
   (if (<= y 3e+56) (/ x (- t (* z a))) (/ (- x (* y z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8.4e+108) {
		tmp = y / a;
	} else if (y <= 3e+56) {
		tmp = x / (t - (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 (y <= (-8.4d+108)) then
        tmp = y / a
    else if (y <= 3d+56) then
        tmp = x / (t - (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 (y <= -8.4e+108) {
		tmp = y / a;
	} else if (y <= 3e+56) {
		tmp = x / (t - (z * a));
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -8.4e+108:
		tmp = y / a
	elif y <= 3e+56:
		tmp = x / (t - (z * a))
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -8.4e+108)
		tmp = Float64(y / a);
	elseif (y <= 3e+56)
		tmp = Float64(x / Float64(t - Float64(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 (y <= -8.4e+108)
		tmp = y / a;
	elseif (y <= 3e+56)
		tmp = x / (t - (z * a));
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8.4e+108], N[(y / a), $MachinePrecision], If[LessEqual[y, 3e+56], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.40000000000000039e108

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in z around inf 65.3%

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

   if -8.40000000000000039e108 < y < 3.00000000000000006e56

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 71.0%

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

      1. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   if 3.00000000000000006e56 < y

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in t around inf 57.8%

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

Alternative 13: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-30} \lor \neg \left(z \leq 950\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e-30) (not (<= z 950.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-30) || !(z <= 950.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1d-30)) .or. (.not. (z <= 950.0d0))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-30) || !(z <= 950.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e-30) or not (z <= 950.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e-30) || !(z <= 950.0))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e-30) || ~((z <= 950.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e-30], N[Not[LessEqual[z, 950.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-30 or 950 < z

   1. Initial program 74.0%

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

      1. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in z around inf 55.8%

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

   if -1e-30 < z < 950

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 58.8%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-30} \lor \neg \left(z \leq 950\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.2% 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 85.8%

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

   1. *-commutative 85.8%

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

3. Simplified 85.8%

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

5. Taylor expanded in z around 0 36.1%

   \[\leadsto \color{blue}{\frac{x}{t}} \]
6. Add Preprocessing

Developer target: 97.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

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

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