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

Percentage Accurate: 85.2% → 97.1%

Time: 11.5s

Alternatives: 13

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% 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: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := t - z \cdot a\\ t_3 := \frac{x - y \cdot z}{t\_2}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(\frac{z}{t\_1} + \frac{x}{y \cdot t\_2}\right)\\ \mathbf{elif}\;t\_3 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot \left(y \cdot z - x\right)}{\frac{t}{z} - a}\\ \mathbf{elif}\;t\_3 \leq 10^{+286}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} + \frac{x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (- t (* z a))) (t_3 (/ (- x (* y z)) t_2)))
   (if (<= t_3 -2e+275)
     (* y (+ (/ z t_1) (/ x (* y t_2))))
     (if (<= t_3 -4e-316)
       t_3
       (if (<= t_3 0.0)
         (/ (* (/ -1.0 z) (- (* y z) x)) (- (/ t z) a))
         (if (<= t_3 1e+286)
           (+ (/ (* y z) t_1) (/ x t_2))
           (/ y (- a (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -2e+275) {
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	} else if (t_3 <= -4e-316) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	} else if (t_3 <= 1e+286) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * a) - t
    t_2 = t - (z * a)
    t_3 = (x - (y * z)) / t_2
    if (t_3 <= (-2d+275)) then
        tmp = y * ((z / t_1) + (x / (y * t_2)))
    else if (t_3 <= (-4d-316)) then
        tmp = t_3
    else if (t_3 <= 0.0d0) then
        tmp = (((-1.0d0) / z) * ((y * z) - x)) / ((t / z) - a)
    else if (t_3 <= 1d+286) then
        tmp = ((y * z) / t_1) + (x / t_2)
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -2e+275) {
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	} else if (t_3 <= -4e-316) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	} else if (t_3 <= 1e+286) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = t - (z * a)
	t_3 = (x - (y * z)) / t_2
	tmp = 0
	if t_3 <= -2e+275:
		tmp = y * ((z / t_1) + (x / (y * t_2)))
	elif t_3 <= -4e-316:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a)
	elif t_3 <= 1e+286:
		tmp = ((y * z) / t_1) + (x / t_2)
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_2)
	tmp = 0.0
	if (t_3 <= -2e+275)
		tmp = Float64(y * Float64(Float64(z / t_1) + Float64(x / Float64(y * t_2))));
	elseif (t_3 <= -4e-316)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(-1.0 / z) * Float64(Float64(y * z) - x)) / Float64(Float64(t / z) - a));
	elseif (t_3 <= 1e+286)
		tmp = Float64(Float64(Float64(y * z) / t_1) + Float64(x / t_2));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = t - (z * a);
	t_3 = (x - (y * z)) / t_2;
	tmp = 0.0;
	if (t_3 <= -2e+275)
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	elseif (t_3 <= -4e-316)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	elseif (t_3 <= 1e+286)
		tmp = ((y * z) / t_1) + (x / t_2);
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+275], N[(y * N[(N[(z / t$95$1), $MachinePrecision] + N[(x / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -4e-316], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(N[(-1.0 / z), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+286], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.99999999999999992e275

   1. Initial program 64.9%

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

      1. *-commutative 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around inf 99.8%

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

   7. Simplified 99.8%

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

   if -1.99999999999999992e275 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.999999984e-316

   1. Initial program 99.6%

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

   if -3.999999984e-316 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. *-un-lft-identity 48.8%

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

      2. times-frac 99.7%

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

      3. *-commutative 99.7%

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

   7. Applied egg-rr 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   9. Simplified 99.8%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000003e286

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

   if 1.00000000000000003e286 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 31.7%

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

      1. *-commutative 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

   6. Taylor expanded in x around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

   8. Simplified 95.7%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot \left(y \cdot z - x\right)}{\frac{t}{z} - a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+286}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot t\_1}\right)\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot \left(y \cdot z - x\right)}{\frac{t}{z} - a}\\ \mathbf{elif}\;t\_2 \leq 10^{+286}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

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 -2e+275)
     (* y (+ (/ z (- (* z a) t)) (/ x (* y t_1))))
     (if (<= t_2 -4e-316)
       t_2
       (if (<= t_2 0.0)
         (/ (* (/ -1.0 z) (- (* y z) x)) (- (/ t z) a))
         (if (<= t_2 1e+286) t_2 (/ y (- a (/ t z)))))))))

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 <= -2e+275) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	} else if (t_2 <= -4e-316) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	} else if (t_2 <= 1e+286) {
		tmp = t_2;
	} else {
		tmp = y / (a - (t / z));
	}
	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 - (z * a)
    t_2 = (x - (y * z)) / t_1
    if (t_2 <= (-2d+275)) then
        tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)))
    else if (t_2 <= (-4d-316)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = (((-1.0d0) / z) * ((y * z) - x)) / ((t / z) - a)
    else if (t_2 <= 1d+286) then
        tmp = t_2
    else
        tmp = y / (a - (t / z))
    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 - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -2e+275) {
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	} else if (t_2 <= -4e-316) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	} else if (t_2 <= 1e+286) {
		tmp = t_2;
	} else {
		tmp = y / (a - (t / z));
	}
	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 <= -2e+275:
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)))
	elif t_2 <= -4e-316:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a)
	elif t_2 <= 1e+286:
		tmp = t_2
	else:
		tmp = y / (a - (t / z))
	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 <= -2e+275)
		tmp = Float64(y * Float64(Float64(z / Float64(Float64(z * a) - t)) + Float64(x / Float64(y * t_1))));
	elseif (t_2 <= -4e-316)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(-1.0 / z) * Float64(Float64(y * z) - x)) / Float64(Float64(t / z) - a));
	elseif (t_2 <= 1e+286)
		tmp = t_2;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	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 <= -2e+275)
		tmp = y * ((z / ((z * a) - t)) + (x / (y * t_1)));
	elseif (t_2 <= -4e-316)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	elseif (t_2 <= 1e+286)
		tmp = t_2;
	else
		tmp = y / (a - (t / z));
	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, -2e+275], 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, -4e-316], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(-1.0 / z), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+286], t$95$2, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.99999999999999992e275

   1. Initial program 64.9%

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

      1. *-commutative 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around inf 99.8%

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

   7. Simplified 99.8%

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

   if -1.99999999999999992e275 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.999999984e-316 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000003e286

   1. Initial program 99.6%

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

   if -3.999999984e-316 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. *-un-lft-identity 48.8%

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

      2. times-frac 99.7%

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

      3. *-commutative 99.7%

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

   7. Applied egg-rr 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   9. Simplified 99.8%

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

   if 1.00000000000000003e286 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 31.7%

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

      1. *-commutative 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

   6. Taylor expanded in x around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

   8. Simplified 95.7%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot \left(y \cdot z - x\right)}{\frac{t}{z} - a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+286}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot \left(y \cdot z - x\right)}{\frac{t}{z} - a}\\ \mathbf{elif}\;t\_1 \leq 10^{+286}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 -4e-316)
     t_1
     (if (<= t_1 0.0)
       (/ (* (/ -1.0 z) (- (* y z) x)) (- (/ t z) a))
       (if (<= t_1 1e+286) t_1 (/ y (- a (/ t z))))))))

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 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	} else if (t_1 <= 1e+286) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (z * a))
    if (t_1 <= (-4d-316)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (((-1.0d0) / z) * ((y * z) - x)) / ((t / z) - a)
    else if (t_1 <= 1d+286) then
        tmp = t_1
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	} else if (t_1 <= 1e+286) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -4e-316:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a)
	elif t_1 <= 1e+286:
		tmp = t_1
	else:
		tmp = y / (a - (t / z))
	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 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-1.0 / z) * Float64(Float64(y * z) - x)) / Float64(Float64(t / z) - a));
	elseif (t_1 <= 1e+286)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	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 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((-1.0 / z) * ((y * z) - x)) / ((t / z) - a);
	elseif (t_1 <= 1e+286)
		tmp = t_1;
	else
		tmp = y / (a - (t / z));
	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, -4e-316], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-1.0 / z), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+286], t$95$1, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.999999984e-316 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000003e286

   1. Initial program 96.2%

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

   if -3.999999984e-316 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. *-un-lft-identity 48.8%

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

      2. times-frac 99.7%

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

      3. *-commutative 99.7%

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

   7. Applied egg-rr 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   9. Simplified 99.8%

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

   if 1.00000000000000003e286 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 31.7%

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

      1. *-commutative 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

   6. Taylor expanded in x around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

   8. Simplified 95.7%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot \left(y \cdot z - x\right)}{\frac{t}{z} - a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+286}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{a + t \cdot \frac{-1}{z}}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+35)
   (/ y (+ a (* t (/ -1.0 z))))
   (if (<= z -1.4e-47)
     (/ x (- t (* z a)))
     (if (<= z 1.3e+27) (/ (- x (* y z)) t) (/ (- y (/ x z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+35) {
		tmp = y / (a + (t * (-1.0 / z)));
	} else if (z <= -1.4e-47) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.3e+27) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d+35)) then
        tmp = y / (a + (t * ((-1.0d0) / z)))
    else if (z <= (-1.4d-47)) then
        tmp = x / (t - (z * a))
    else if (z <= 1.3d+27) then
        tmp = (x - (y * z)) / t
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+35) {
		tmp = y / (a + (t * (-1.0 / z)));
	} else if (z <= -1.4e-47) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.3e+27) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+35:
		tmp = y / (a + (t * (-1.0 / z)))
	elif z <= -1.4e-47:
		tmp = x / (t - (z * a))
	elif z <= 1.3e+27:
		tmp = (x - (y * z)) / t
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+35)
		tmp = Float64(y / Float64(a + Float64(t * Float64(-1.0 / z))));
	elseif (z <= -1.4e-47)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.3e+27)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+35)
		tmp = y / (a + (t * (-1.0 / z)));
	elseif (z <= -1.4e-47)
		tmp = x / (t - (z * a));
	elseif (z <= 1.3e+27)
		tmp = (x - (y * z)) / t;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+35], N[(y / N[(a + N[(t * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e-47], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+27], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.9999999999999997e35

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in z around inf 60.7%

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

   6. Taylor expanded in x around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. mul-1-neg 85.1%

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

   8. Simplified 85.1%

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

      1. div-inv 85.2%

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

   10. Applied egg-rr 85.2%

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

   if -7.9999999999999997e35 < z < -1.39999999999999996e-47

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 82.2%

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

      1. *-commutative 82.2%

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

   7. Simplified 82.2%

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

   if -1.39999999999999996e-47 < z < 1.30000000000000004e27

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 76.3%

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

   if 1.30000000000000004e27 < z

   1. Initial program 65.5%

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

      1. *-commutative 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in x around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. *-un-lft-identity 65.5%

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

      3. times-frac 71.3%

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

   7. Applied egg-rr 71.3%

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

   8. Taylor expanded in a around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. unsub-neg 78.9%

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

   10. Simplified 78.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{a + t \cdot \frac{-1}{z}}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+35)
   (/ y (- a (/ t z)))
   (if (<= z -3.9e-48)
     (/ x (- t (* z a)))
     (if (<= z 5.1e+30) (/ (- x (* y z)) t) (/ (- y (/ x z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+35) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.9e-48) {
		tmp = x / (t - (z * a));
	} else if (z <= 5.1e+30) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+35)) then
        tmp = y / (a - (t / z))
    else if (z <= (-3.9d-48)) then
        tmp = x / (t - (z * a))
    else if (z <= 5.1d+30) then
        tmp = (x - (y * z)) / t
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+35) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.9e-48) {
		tmp = x / (t - (z * a));
	} else if (z <= 5.1e+30) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+35:
		tmp = y / (a - (t / z))
	elif z <= -3.9e-48:
		tmp = x / (t - (z * a))
	elif z <= 5.1e+30:
		tmp = (x - (y * z)) / t
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+35)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -3.9e-48)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 5.1e+30)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+35)
		tmp = y / (a - (t / z));
	elseif (z <= -3.9e-48)
		tmp = x / (t - (z * a));
	elseif (z <= 5.1e+30)
		tmp = (x - (y * z)) / t;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+35], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-48], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+30], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.50000000000000001e35

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in z around inf 60.7%

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

   6. Taylor expanded in x around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. mul-1-neg 85.1%

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

   8. Simplified 85.1%

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

   if -5.50000000000000001e35 < z < -3.9e-48

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 82.2%

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

      1. *-commutative 82.2%

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

   7. Simplified 82.2%

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

   if -3.9e-48 < z < 5.10000000000000035e30

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 76.3%

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

   if 5.10000000000000035e30 < z

   1. Initial program 65.5%

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

      1. *-commutative 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in x around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. *-un-lft-identity 65.5%

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

      3. times-frac 71.3%

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

   7. Applied egg-rr 71.3%

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

   8. Taylor expanded in a around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. unsub-neg 78.9%

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

   10. Simplified 78.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-24)
   (/ y a)
   (if (<= z 1.12e-97) (/ x t) (if (<= z 6.9e+28) (/ (* y z) (- t)) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-24) {
		tmp = y / a;
	} else if (z <= 1.12e-97) {
		tmp = x / t;
	} else if (z <= 6.9e+28) {
		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 <= (-2.2d-24)) then
        tmp = y / a
    else if (z <= 1.12d-97) then
        tmp = x / t
    else if (z <= 6.9d+28) 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 <= -2.2e-24) {
		tmp = y / a;
	} else if (z <= 1.12e-97) {
		tmp = x / t;
	} else if (z <= 6.9e+28) {
		tmp = (y * z) / -t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-24:
		tmp = y / a
	elif z <= 1.12e-97:
		tmp = x / t
	elif z <= 6.9e+28:
		tmp = (y * z) / -t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-24)
		tmp = Float64(y / a);
	elseif (z <= 1.12e-97)
		tmp = Float64(x / t);
	elseif (z <= 6.9e+28)
		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 <= -2.2e-24)
		tmp = y / a;
	elseif (z <= 1.12e-97)
		tmp = x / t;
	elseif (z <= 6.9e+28)
		tmp = (y * z) / -t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-24], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.12e-97], N[(x / t), $MachinePrecision], If[LessEqual[z, 6.9e+28], N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000002e-24 or 6.9e28 < z

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in z around inf 59.4%

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

   if -2.20000000000000002e-24 < z < 1.12e-97

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 59.6%

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

   if 1.12e-97 < z < 6.9e28

   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 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 59.3%

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

      3. distribute-rgt-neg-in 59.3%

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

      4. distribute-neg-frac2 59.3%

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

      5. cancel-sign-sub-inv 59.3%

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

      6. *-commutative 59.3%

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

      7. +-commutative 59.3%

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

      8. *-commutative 59.3%

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

      9. neg-mul-1 59.3%

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

      10. associate-*r* 59.3%

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

      11. mul-1-neg 59.3%

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

      12. distribute-rgt-neg-in 59.3%

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

      13. fma-undefine 59.3%

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

      14. neg-sub0 59.3%

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

      15. fma-undefine 59.3%

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

      16. distribute-rgt-neg-in 59.3%

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

      17. *-commutative 59.3%

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

      18. distribute-rgt-neg-out 59.3%

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

      19. associate--r+ 59.3%

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

      20. neg-sub0 59.3%

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

      21. distribute-rgt-neg-out 59.3%

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

      22. remove-double-neg 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in z around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. *-commutative 50.3%

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

      3. neg-mul-1 50.3%

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

      4. distribute-rgt-neg-in 50.3%

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

   10. Simplified 50.3%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e-24)
   (/ y a)
   (if (<= z 7.5e-34) (/ x t) (if (<= z 1.8e+31) (* y (/ z (- t))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e-24) {
		tmp = y / a;
	} else if (z <= 7.5e-34) {
		tmp = x / t;
	} else if (z <= 1.8e+31) {
		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 <= (-3.6d-24)) then
        tmp = y / a
    else if (z <= 7.5d-34) then
        tmp = x / t
    else if (z <= 1.8d+31) 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 <= -3.6e-24) {
		tmp = y / a;
	} else if (z <= 7.5e-34) {
		tmp = x / t;
	} else if (z <= 1.8e+31) {
		tmp = y * (z / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e-24:
		tmp = y / a
	elif z <= 7.5e-34:
		tmp = x / t
	elif z <= 1.8e+31:
		tmp = y * (z / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e-24)
		tmp = Float64(y / a);
	elseif (z <= 7.5e-34)
		tmp = Float64(x / t);
	elseif (z <= 1.8e+31)
		tmp = Float64(y * Float64(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 <= -3.6e-24)
		tmp = y / a;
	elseif (z <= 7.5e-34)
		tmp = x / t;
	elseif (z <= 1.8e+31)
		tmp = y * (z / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e-24], N[(y / a), $MachinePrecision], If[LessEqual[z, 7.5e-34], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.8e+31], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6000000000000001e-24 or 1.79999999999999998e31 < z

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in z around inf 59.4%

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

   if -3.6000000000000001e-24 < z < 7.5000000000000004e-34

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 57.1%

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

   if 7.5000000000000004e-34 < z < 1.79999999999999998e31

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-/l* 74.2%

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

      3. distribute-rgt-neg-in 74.2%

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

      4. distribute-neg-frac2 74.2%

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

      5. cancel-sign-sub-inv 74.2%

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

      6. *-commutative 74.2%

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

      7. +-commutative 74.2%

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

      8. *-commutative 74.2%

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

      9. neg-mul-1 74.2%

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

      10. associate-*r* 74.2%

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

      11. mul-1-neg 74.2%

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

      12. distribute-rgt-neg-in 74.2%

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

      13. fma-undefine 74.2%

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

      14. neg-sub0 74.2%

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

      15. fma-undefine 74.2%

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

      16. distribute-rgt-neg-in 74.2%

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

      17. *-commutative 74.2%

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

      18. distribute-rgt-neg-out 74.2%

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

      19. associate--r+ 74.2%

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

      20. neg-sub0 74.2%

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

      21. distribute-rgt-neg-out 74.2%

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

      22. remove-double-neg 74.2%

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

   7. Simplified 74.2%

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

   8. Taylor expanded in z around 0 64.7%

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

      1. associate-*r/ 64.7%

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

      2. mul-1-neg 64.7%

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

   10. Simplified 64.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{a + t \cdot \frac{-1}{z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+136)
   (/ y (+ a (* t (/ -1.0 z))))
   (if (<= z 4.5e+144) (/ (- x (* y z)) (- t (* z a))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+136) {
		tmp = y / (a + (t * (-1.0 / z)));
	} else if (z <= 4.5e+144) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+136)) then
        tmp = y / (a + (t * ((-1.0d0) / z)))
    else if (z <= 4.5d+144) then
        tmp = (x - (y * z)) / (t - (z * a))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+136) {
		tmp = y / (a + (t * (-1.0 / z)));
	} else if (z <= 4.5e+144) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+136:
		tmp = y / (a + (t * (-1.0 / z)))
	elif z <= 4.5e+144:
		tmp = (x - (y * z)) / (t - (z * a))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+136)
		tmp = Float64(y / Float64(a + Float64(t * Float64(-1.0 / z))));
	elseif (z <= 4.5e+144)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+136)
		tmp = y / (a + (t * (-1.0 / z)));
	elseif (z <= 4.5e+144)
		tmp = (x - (y * z)) / (t - (z * a));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+136], N[(y / N[(a + N[(t * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+144], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999993e136

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.7%

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

   6. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. mul-1-neg 89.4%

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

   8. Simplified 89.4%

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

      1. div-inv 89.5%

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

   10. Applied egg-rr 89.5%

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

   if -6.79999999999999993e136 < z < 4.49999999999999967e144

   1. Initial program 95.5%

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

   if 4.49999999999999967e144 < z

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in x around 0 60.9%

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

      1. *-commutative 60.9%

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

      2. *-un-lft-identity 60.9%

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

      3. times-frac 67.3%

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

   7. Applied egg-rr 67.3%

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

   8. Taylor expanded in a around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. unsub-neg 87.1%

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

   10. Simplified 87.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{a + t \cdot \frac{-1}{z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+77} \lor \neg \left(z \leq 6.5 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.6e+77) (not (<= z 6.5e+28)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.6e+77) || !(z <= 6.5e+28)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.6d+77)) .or. (.not. (z <= 6.5d+28))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.6e+77) || !(z <= 6.5e+28)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.6e+77) or not (z <= 6.5e+28):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.6e+77) || !(z <= 6.5e+28))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.6e+77) || ~((z <= 6.5e+28)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.6e+77], N[Not[LessEqual[z, 6.5e+28]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999999e77 or 6.5000000000000001e28 < z

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in x around 0 61.5%

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

      1. *-commutative 61.5%

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

      2. *-un-lft-identity 61.5%

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

      3. times-frac 62.2%

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

   7. Applied egg-rr 62.2%

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

   8. Taylor expanded in a around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   10. Simplified 80.5%

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

   if -4.5999999999999999e77 < z < 6.5000000000000001e28

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 74.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+77} \lor \neg \left(z \leq 6.5 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+80} \lor \neg \left(z \leq 8.5 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+80) (not (<= z 8.5e+92))) (/ y a) (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+80) || !(z <= 8.5e+92)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+80)) .or. (.not. (z <= 8.5d+92))) then
        tmp = y / a
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+80) || !(z <= 8.5e+92)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+80) or not (z <= 8.5e+92):
		tmp = y / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+80) || !(z <= 8.5e+92))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+80) || ~((z <= 8.5e+92)))
		tmp = y / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+80], N[Not[LessEqual[z, 8.5e+92]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999982e80 or 8.5000000000000001e92 < z

   1. Initial program 59.9%

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

      1. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in z around inf 65.6%

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

   if -2.59999999999999982e80 < z < 8.5000000000000001e92

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 72.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+80} \lor \neg \left(z \leq 8.5 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+40} \lor \neg \left(z \leq 3.35 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e+40) (not (<= z 3.35e+22))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+40) || !(z <= 3.35e+22)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.15d+40)) .or. (.not. (z <= 3.35d+22))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+40) || !(z <= 3.35e+22)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e+40) or not (z <= 3.35e+22):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e+40) || !(z <= 3.35e+22))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e+40) || ~((z <= 3.35e+22)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e+40], N[Not[LessEqual[z, 3.35e+22]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1500000000000001e40 or 3.3500000000000001e22 < z

   1. Initial program 63.0%

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

      1. *-commutative 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in z around inf 62.6%

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

   if -2.1500000000000001e40 < z < 3.3500000000000001e22

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 71.5%

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

      1. *-commutative 71.5%

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

   7. Simplified 71.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+40} \lor \neg \left(z \leq 3.35 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-22} \lor \neg \left(z \leq 2.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e-22) (not (<= z 2.8e+22))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e-22) || !(z <= 2.8e+22)) {
		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 <= (-1.05d-22)) .or. (.not. (z <= 2.8d+22))) 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 <= -1.05e-22) || !(z <= 2.8e+22)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e-22) or not (z <= 2.8e+22):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e-22) || !(z <= 2.8e+22))
		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 <= -1.05e-22) || ~((z <= 2.8e+22)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e-22], N[Not[LessEqual[z, 2.8e+22]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004e-22 or 2.8e22 < z

   1. Initial program 65.7%

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

      1. *-commutative 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in z around inf 58.9%

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

   if -1.05000000000000004e-22 < z < 2.8e22

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 54.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-22} \lor \neg \left(z \leq 2.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. *-commutative 83.8%

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

3. Simplified 83.8%

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

5. Taylor expanded in z around 0 35.4%

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

Developer Target 1: 97.3% 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 2024123 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 4392440296622287/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))))))

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