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

Percentage Accurate: 85.7% → 98.0%

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: 85.7% 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: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y \cdot z - x}{t\_1}\\ t_3 := \frac{x}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{t\_1} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x - y \cdot z}{a - \frac{t}{z}}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} - t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ (- (* y z) x) t_1)) (t_3 (/ x t_1)))
   (if (<= t_2 (- INFINITY))
     (* y (+ (/ z t_1) (/ x (* y (- t (* z a))))))
     (if (<= t_2 -1e-306)
       t_2
       (if (<= t_2 0.0)
         (* (/ -1.0 z) (/ (- x (* y z)) (- a (/ t z))))
         (if (<= t_2 5e+293) (- (/ (* y z) t_1) t_3) (- (/ y a) t_3)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = ((y * z) - x) / t_1;
	double t_3 = x / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y * ((z / t_1) + (x / (y * (t - (z * a)))));
	} else if (t_2 <= -1e-306) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	} else if (t_2 <= 5e+293) {
		tmp = ((y * z) / t_1) - t_3;
	} else {
		tmp = (y / a) - t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = ((y * z) - x) / t_1;
	double t_3 = x / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z / t_1) + (x / (y * (t - (z * a)))));
	} else if (t_2 <= -1e-306) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	} else if (t_2 <= 5e+293) {
		tmp = ((y * z) / t_1) - t_3;
	} else {
		tmp = (y / a) - t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = ((y * z) - x) / t_1
	t_3 = x / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y * ((z / t_1) + (x / (y * (t - (z * a)))))
	elif t_2 <= -1e-306:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)))
	elif t_2 <= 5e+293:
		tmp = ((y * z) / t_1) - t_3
	else:
		tmp = (y / a) - t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(Float64(y * z) - x) / t_1)
	t_3 = Float64(x / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z / t_1) + Float64(x / Float64(y * Float64(t - Float64(z * a))))));
	elseif (t_2 <= -1e-306)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-1.0 / z) * Float64(Float64(x - Float64(y * z)) / Float64(a - Float64(t / z))));
	elseif (t_2 <= 5e+293)
		tmp = Float64(Float64(Float64(y * z) / t_1) - t_3);
	else
		tmp = Float64(Float64(y / a) - t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = ((y * z) - x) / t_1;
	t_3 = x / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y * ((z / t_1) + (x / (y * (t - (z * a)))));
	elseif (t_2 <= -1e-306)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	elseif (t_2 <= 5e+293)
		tmp = ((y * z) / t_1) - t_3;
	else
		tmp = (y / a) - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y * N[(N[(z / t$95$1), $MachinePrecision] + N[(x / N[(y * N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-306], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(-1.0 / z), $MachinePrecision] * N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+293], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] - t$95$3), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 62.3%

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

      1. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in y around inf 99.8%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000000000003e-306

   1. Initial program 99.6%

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

   if -1.00000000000000003e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in z around inf 72.8%

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

      1. *-un-lft-identity 72.8%

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

      2. times-frac 99.8%

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

   7. Applied egg-rr 99.8%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.00000000000000033e293

   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 5.00000000000000033e293 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 36.3%

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

      1. *-commutative 36.3%

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

   3. Simplified 36.3%

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

   5. Taylor expanded in x around 0 36.3%

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

   6. Taylor expanded in z around inf 89.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot z - x}{z \cdot a - t} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{y \cdot z - x}{z \cdot a - t} \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{y \cdot z - x}{z \cdot a - t} \leq 0:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x - y \cdot z}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{y \cdot z - x}{z \cdot a - t} \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x}{t\_1}\\ t_3 := \frac{y \cdot z - x}{t\_1}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x - y \cdot z}{a - \frac{t}{z}}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} - t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ x t_1)) (t_3 (/ (- (* y z) x) t_1)))
   (if (<= t_3 -1e-306)
     t_3
     (if (<= t_3 0.0)
       (* (/ -1.0 z) (/ (- x (* y z)) (- a (/ t z))))
       (if (<= t_3 5e+293) (- (/ (* y z) t_1) t_2) (- (/ y a) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = x / t_1;
	double t_3 = ((y * z) - x) / t_1;
	double tmp;
	if (t_3 <= -1e-306) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	} else if (t_3 <= 5e+293) {
		tmp = ((y * z) / t_1) - t_2;
	} else {
		tmp = (y / a) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * a) - t
    t_2 = x / t_1
    t_3 = ((y * z) - x) / t_1
    if (t_3 <= (-1d-306)) then
        tmp = t_3
    else if (t_3 <= 0.0d0) then
        tmp = ((-1.0d0) / z) * ((x - (y * z)) / (a - (t / z)))
    else if (t_3 <= 5d+293) then
        tmp = ((y * z) / t_1) - t_2
    else
        tmp = (y / a) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = x / t_1;
	double t_3 = ((y * z) - x) / t_1;
	double tmp;
	if (t_3 <= -1e-306) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	} else if (t_3 <= 5e+293) {
		tmp = ((y * z) / t_1) - t_2;
	} else {
		tmp = (y / a) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = x / t_1
	t_3 = ((y * z) - x) / t_1
	tmp = 0
	if t_3 <= -1e-306:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)))
	elif t_3 <= 5e+293:
		tmp = ((y * z) / t_1) - t_2
	else:
		tmp = (y / a) - t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(x / t_1)
	t_3 = Float64(Float64(Float64(y * z) - x) / t_1)
	tmp = 0.0
	if (t_3 <= -1e-306)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(-1.0 / z) * Float64(Float64(x - Float64(y * z)) / Float64(a - Float64(t / z))));
	elseif (t_3 <= 5e+293)
		tmp = Float64(Float64(Float64(y * z) / t_1) - t_2);
	else
		tmp = Float64(Float64(y / a) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = x / t_1;
	t_3 = ((y * z) - x) / t_1;
	tmp = 0.0;
	if (t_3 <= -1e-306)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	elseif (t_3 <= 5e+293)
		tmp = ((y * z) / t_1) - t_2;
	else
		tmp = (y / a) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-306], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(-1.0 / z), $MachinePrecision] * N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+293], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000000000003e-306

   1. Initial program 93.1%

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

   if -1.00000000000000003e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in z around inf 72.8%

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

      1. *-un-lft-identity 72.8%

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

      2. times-frac 99.8%

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

   7. Applied egg-rr 99.8%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.00000000000000033e293

   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 5.00000000000000033e293 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 36.3%

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

      1. *-commutative 36.3%

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

   3. Simplified 36.3%

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

   5. Taylor expanded in x around 0 36.3%

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

   6. Taylor expanded in z around inf 89.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot z - x}{z \cdot a - t} \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{y \cdot z - x}{z \cdot a - t} \leq 0:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x - y \cdot z}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{y \cdot z - x}{z \cdot a - t} \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y \cdot z - x}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x - y \cdot z}{a - \frac{t}{z}}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ (- (* y z) x) t_1)))
   (if (<= t_2 -1e-306)
     t_2
     (if (<= t_2 0.0)
       (* (/ -1.0 z) (/ (- x (* y z)) (- a (/ t z))))
       (if (<= t_2 5e+293) t_2 (- (/ y a) (/ x t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = ((y * z) - x) / t_1;
	double tmp;
	if (t_2 <= -1e-306) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	} else if (t_2 <= 5e+293) {
		tmp = t_2;
	} else {
		tmp = (y / a) - (x / t_1);
	}
	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 = (z * a) - t
    t_2 = ((y * z) - x) / t_1
    if (t_2 <= (-1d-306)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = ((-1.0d0) / z) * ((x - (y * z)) / (a - (t / z)))
    else if (t_2 <= 5d+293) then
        tmp = t_2
    else
        tmp = (y / a) - (x / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = ((y * z) - x) / t_1;
	double tmp;
	if (t_2 <= -1e-306) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	} else if (t_2 <= 5e+293) {
		tmp = t_2;
	} else {
		tmp = (y / a) - (x / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = ((y * z) - x) / t_1
	tmp = 0
	if t_2 <= -1e-306:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)))
	elif t_2 <= 5e+293:
		tmp = t_2
	else:
		tmp = (y / a) - (x / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(Float64(y * z) - x) / t_1)
	tmp = 0.0
	if (t_2 <= -1e-306)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-1.0 / z) * Float64(Float64(x - Float64(y * z)) / Float64(a - Float64(t / z))));
	elseif (t_2 <= 5e+293)
		tmp = t_2;
	else
		tmp = Float64(Float64(y / a) - Float64(x / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = ((y * z) - x) / t_1;
	tmp = 0.0;
	if (t_2 <= -1e-306)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (-1.0 / z) * ((x - (y * z)) / (a - (t / z)));
	elseif (t_2 <= 5e+293)
		tmp = t_2;
	else
		tmp = (y / a) - (x / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-306], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(-1.0 / z), $MachinePrecision] * N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+293], t$95$2, N[(N[(y / a), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000000000003e-306 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.00000000000000033e293

   1. Initial program 95.6%

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

   if -1.00000000000000003e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in z around inf 72.8%

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

      1. *-un-lft-identity 72.8%

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

      2. times-frac 99.8%

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

   7. Applied egg-rr 99.8%

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

   if 5.00000000000000033e293 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 36.3%

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

      1. *-commutative 36.3%

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

   3. Simplified 36.3%

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

   5. Taylor expanded in x around 0 36.3%

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

   6. Taylor expanded in z around inf 89.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot z - x}{z \cdot a - t} \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{y \cdot z - x}{z \cdot a - t} \leq 0:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x - y \cdot z}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{y \cdot z - x}{z \cdot a - t} \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{y \cdot z - x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} + x \cdot \frac{-1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)))
   (if (<= z -1.45e+98)
     (/ y (- a (/ t z)))
     (if (<= z 6.8e+72)
       (/ (- (* y z) x) t_1)
       (+ (/ y a) (* x (/ -1.0 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double tmp;
	if (z <= -1.45e+98) {
		tmp = y / (a - (t / z));
	} else if (z <= 6.8e+72) {
		tmp = ((y * z) - x) / t_1;
	} else {
		tmp = (y / a) + (x * (-1.0 / t_1));
	}
	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 = (z * a) - t
    if (z <= (-1.45d+98)) then
        tmp = y / (a - (t / z))
    else if (z <= 6.8d+72) then
        tmp = ((y * z) - x) / t_1
    else
        tmp = (y / a) + (x * ((-1.0d0) / t_1))
    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 tmp;
	if (z <= -1.45e+98) {
		tmp = y / (a - (t / z));
	} else if (z <= 6.8e+72) {
		tmp = ((y * z) - x) / t_1;
	} else {
		tmp = (y / a) + (x * (-1.0 / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	tmp = 0
	if z <= -1.45e+98:
		tmp = y / (a - (t / z))
	elif z <= 6.8e+72:
		tmp = ((y * z) - x) / t_1
	else:
		tmp = (y / a) + (x * (-1.0 / t_1))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	tmp = 0.0
	if (z <= -1.45e+98)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 6.8e+72)
		tmp = Float64(Float64(Float64(y * z) - x) / t_1);
	else
		tmp = Float64(Float64(y / a) + Float64(x * Float64(-1.0 / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	tmp = 0.0;
	if (z <= -1.45e+98)
		tmp = y / (a - (t / z));
	elseif (z <= 6.8e+72)
		tmp = ((y * z) - x) / t_1;
	else
		tmp = (y / a) + (x * (-1.0 / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[z, -1.45e+98], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+72], N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(y / a), $MachinePrecision] + N[(x * N[(-1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000005e98

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

   3. Simplified 49.0%

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

   5. Taylor expanded in z around inf 49.0%

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

   6. Taylor expanded in x around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. mul-1-neg 84.1%

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

   8. Simplified 84.1%

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

   if -1.45000000000000005e98 < z < 6.7999999999999997e72

   1. Initial program 98.6%

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

   if 6.7999999999999997e72 < z

   1. Initial program 65.6%

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

      1. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in x around 0 65.6%

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

   6. Taylor expanded in z around inf 83.9%

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

      1. div-inv 84.0%

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

      2. *-commutative 84.0%

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

   8. Applied egg-rr 84.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} + x \cdot \frac{-1}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+64} \lor \neg \left(t \leq 9.5 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.8e+64) (not (<= t 9.5e+67)))
   (/ (- x (* y z)) t)
   (- (/ y a) (/ x (- (* z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.8e+64) || !(t <= 9.5e+67)) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y / a) - (x / ((z * a) - 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 ((t <= (-6.8d+64)) .or. (.not. (t <= 9.5d+67))) then
        tmp = (x - (y * z)) / t
    else
        tmp = (y / a) - (x / ((z * a) - 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 ((t <= -6.8e+64) || !(t <= 9.5e+67)) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y / a) - (x / ((z * a) - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.8e+64) or not (t <= 9.5e+67):
		tmp = (x - (y * z)) / t
	else:
		tmp = (y / a) - (x / ((z * a) - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.8e+64) || !(t <= 9.5e+67))
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(Float64(y / a) - Float64(x / Float64(Float64(z * a) - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.8e+64) || ~((t <= 9.5e+67)))
		tmp = (x - (y * z)) / t;
	else
		tmp = (y / a) - (x / ((z * a) - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.8e+64], N[Not[LessEqual[t, 9.5e+67]], $MachinePrecision]], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - N[(x / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8000000000000003e64 or 9.5000000000000002e67 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 75.5%

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

      1. *-commutative 75.5%

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

   7. Simplified 75.5%

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

   if -6.8000000000000003e64 < t < 9.5000000000000002e67

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in x around 0 84.4%

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

   6. Taylor expanded in z around inf 90.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+64} \lor \neg \left(t \leq 9.5 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e-93)
   (/ y a)
   (if (<= z 4e-32) (/ x t) (if (<= z 1.02e+29) (* z (/ y (- t))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-93) {
		tmp = y / a;
	} else if (z <= 4e-32) {
		tmp = x / t;
	} else if (z <= 1.02e+29) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d-93)) then
        tmp = y / a
    else if (z <= 4d-32) then
        tmp = x / t
    else if (z <= 1.02d+29) then
        tmp = z * (y / -t)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-93) {
		tmp = y / a;
	} else if (z <= 4e-32) {
		tmp = x / t;
	} else if (z <= 1.02e+29) {
		tmp = z * (y / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e-93:
		tmp = y / a
	elif z <= 4e-32:
		tmp = x / t
	elif z <= 1.02e+29:
		tmp = z * (y / -t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e-93)
		tmp = Float64(y / a);
	elseif (z <= 4e-32)
		tmp = Float64(x / t);
	elseif (z <= 1.02e+29)
		tmp = Float64(z * Float64(y / 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 <= -1.15e-93)
		tmp = y / a;
	elseif (z <= 4e-32)
		tmp = x / t;
	elseif (z <= 1.02e+29)
		tmp = z * (y / -t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e-93], N[(y / a), $MachinePrecision], If[LessEqual[z, 4e-32], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.02e+29], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e-93 or 1.0200000000000001e29 < z

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in z around inf 56.2%

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

   if -1.1499999999999999e-93 < z < 4.00000000000000022e-32

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 69.1%

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

   if 4.00000000000000022e-32 < z < 1.0200000000000001e29

   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 70.6%

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

      1. mul-1-neg 70.6%

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

      2. associate-/l* 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. sub-neg 70.5%

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

      5. mul-1-neg 70.5%

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

      6. +-commutative 70.5%

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

      7. mul-1-neg 70.5%

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

      8. distribute-rgt-neg-in 70.5%

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

      9. fma-undefine 70.5%

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

      10. distribute-neg-frac2 70.5%

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

      11. neg-sub0 70.5%

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

      12. fma-undefine 70.5%

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

      13. distribute-rgt-neg-in 70.5%

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

      14. distribute-lft-neg-in 70.5%

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

      15. *-commutative 70.5%

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

      16. associate--r+ 70.5%

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

      17. neg-sub0 70.5%

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

      18. distribute-rgt-neg-out 70.5%

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

      19. remove-double-neg 70.5%

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

      20. *-commutative 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in z around 0 64.0%

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

      1. associate-*r/ 64.0%

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

      2. neg-mul-1 64.0%

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

   10. Simplified 64.0%

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

   11. Taylor expanded in y around 0 64.1%

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

       1. mul-1-neg 64.1%

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

       2. *-commutative 64.1%

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

       3. associate-/l* 64.1%

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

       4. distribute-lft-neg-in 64.1%

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

   13. Simplified 64.1%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e-95)
   (/ y a)
   (if (<= z 3e-40) (/ x t) (if (<= z 1.22e+29) (* y (/ z (- t))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e-95) {
		tmp = y / a;
	} else if (z <= 3e-40) {
		tmp = x / t;
	} else if (z <= 1.22e+29) {
		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-95)) then
        tmp = y / a
    else if (z <= 3d-40) then
        tmp = x / t
    else if (z <= 1.22d+29) 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-95) {
		tmp = y / a;
	} else if (z <= 3e-40) {
		tmp = x / t;
	} else if (z <= 1.22e+29) {
		tmp = y * (z / -t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e-95:
		tmp = y / a
	elif z <= 3e-40:
		tmp = x / t
	elif z <= 1.22e+29:
		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-95)
		tmp = Float64(y / a);
	elseif (z <= 3e-40)
		tmp = Float64(x / t);
	elseif (z <= 1.22e+29)
		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-95)
		tmp = y / a;
	elseif (z <= 3e-40)
		tmp = x / t;
	elseif (z <= 1.22e+29)
		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-95], N[(y / a), $MachinePrecision], If[LessEqual[z, 3e-40], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.22e+29], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-95 or 1.22e29 < z

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in z around inf 56.2%

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

   if -3.6e-95 < z < 3.0000000000000002e-40

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 69.1%

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

   if 3.0000000000000002e-40 < z < 1.22e29

   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 70.6%

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

      1. mul-1-neg 70.6%

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

      2. associate-/l* 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. sub-neg 70.5%

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

      5. mul-1-neg 70.5%

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

      6. +-commutative 70.5%

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

      7. mul-1-neg 70.5%

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

      8. distribute-rgt-neg-in 70.5%

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

      9. fma-undefine 70.5%

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

      10. distribute-neg-frac2 70.5%

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

      11. neg-sub0 70.5%

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

      12. fma-undefine 70.5%

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

      13. distribute-rgt-neg-in 70.5%

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

      14. distribute-lft-neg-in 70.5%

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

      15. *-commutative 70.5%

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

      16. associate--r+ 70.5%

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

      17. neg-sub0 70.5%

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

      18. distribute-rgt-neg-out 70.5%

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

      19. remove-double-neg 70.5%

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

      20. *-commutative 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in z around 0 64.0%

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

      1. associate-*r/ 64.0%

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

      2. neg-mul-1 64.0%

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

   10. Simplified 64.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+74}:\\ \;\;\;\;\frac{y \cdot z - x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)))
   (if (<= z -1.45e+98)
     (/ y (- a (/ t z)))
     (if (<= z 1.95e+74) (/ (- (* y z) x) t_1) (- (/ y a) (/ x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double tmp;
	if (z <= -1.45e+98) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.95e+74) {
		tmp = ((y * z) - x) / t_1;
	} else {
		tmp = (y / a) - (x / t_1);
	}
	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 = (z * a) - t
    if (z <= (-1.45d+98)) then
        tmp = y / (a - (t / z))
    else if (z <= 1.95d+74) then
        tmp = ((y * z) - x) / t_1
    else
        tmp = (y / a) - (x / t_1)
    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 tmp;
	if (z <= -1.45e+98) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.95e+74) {
		tmp = ((y * z) - x) / t_1;
	} else {
		tmp = (y / a) - (x / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	tmp = 0
	if z <= -1.45e+98:
		tmp = y / (a - (t / z))
	elif z <= 1.95e+74:
		tmp = ((y * z) - x) / t_1
	else:
		tmp = (y / a) - (x / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	tmp = 0.0
	if (z <= -1.45e+98)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 1.95e+74)
		tmp = Float64(Float64(Float64(y * z) - x) / t_1);
	else
		tmp = Float64(Float64(y / a) - Float64(x / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	tmp = 0.0;
	if (z <= -1.45e+98)
		tmp = y / (a - (t / z));
	elseif (z <= 1.95e+74)
		tmp = ((y * z) - x) / t_1;
	else
		tmp = (y / a) - (x / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[z, -1.45e+98], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+74], N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000005e98

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

   3. Simplified 49.0%

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

   5. Taylor expanded in z around inf 49.0%

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

   6. Taylor expanded in x around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. mul-1-neg 84.1%

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

   8. Simplified 84.1%

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

   if -1.45000000000000005e98 < z < 1.95000000000000004e74

   1. Initial program 98.6%

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

   if 1.95000000000000004e74 < z

   1. Initial program 65.6%

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

      1. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in x around 0 65.6%

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

   6. Taylor expanded in z around inf 83.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+74}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93} \lor \neg \left(z \leq 4.7\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-93) (not (<= z 4.7)))
   (/ (- y (/ x z)) a)
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-93) || !(z <= 4.7)) {
		tmp = (y - (x / z)) / 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 <= (-1.15d-93)) .or. (.not. (z <= 4.7d0))) then
        tmp = (y - (x / z)) / 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 <= -1.15e-93) || !(z <= 4.7)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-93) or not (z <= 4.7):
		tmp = (y - (x / z)) / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-93) || !(z <= 4.7))
		tmp = Float64(Float64(y - Float64(x / z)) / 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 <= -1.15e-93) || ~((z <= 4.7)))
		tmp = (y - (x / z)) / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-93], N[Not[LessEqual[z, 4.7]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e-93 or 4.70000000000000018 < z

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in z around inf 73.8%

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

   6. Taylor expanded in t around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. distribute-frac-neg 74.1%

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

      3. sub-neg 74.1%

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

      4. +-commutative 74.1%

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

      5. distribute-neg-in 74.1%

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

      6. remove-double-neg 74.1%

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

      7. unsub-neg 74.1%

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

   8. Simplified 74.1%

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

   if -1.1499999999999999e-93 < z < 4.70000000000000018

   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 84.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93} \lor \neg \left(z \leq 4.7\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+97} \lor \neg \left(z \leq 7600\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.15e+97) (not (<= z 7600.0))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.15e+97) || !(z <= 7600.0)) {
		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 <= (-3.15d+97)) .or. (.not. (z <= 7600.0d0))) 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 <= -3.15e+97) || !(z <= 7600.0)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.15e+97) or not (z <= 7600.0):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.15e+97) || !(z <= 7600.0))
		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 <= -3.15e+97) || ~((z <= 7600.0)))
		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, -3.15e+97], N[Not[LessEqual[z, 7600.0]], $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 < -3.14999999999999999e97 or 7600 < 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 z around inf 63.8%

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

   if -3.14999999999999999e97 < z < 7600

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 76.7%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+97} \lor \neg \left(z \leq 7600\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e-93)
   (/ (- y (/ x z)) a)
   (if (<= z 7e-12) (/ x (- t (* z a))) (/ y (- a (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-93) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 7e-12) {
		tmp = x / (t - (z * a));
	} 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) :: tmp
    if (z <= (-1.15d-93)) then
        tmp = (y - (x / z)) / a
    else if (z <= 7d-12) then
        tmp = x / (t - (z * a))
    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 tmp;
	if (z <= -1.15e-93) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 7e-12) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e-93:
		tmp = (y - (x / z)) / a
	elif z <= 7e-12:
		tmp = x / (t - (z * a))
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e-93)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (z <= 7e-12)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e-93)
		tmp = (y - (x / z)) / a;
	elseif (z <= 7e-12)
		tmp = x / (t - (z * a));
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e-93], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 7e-12], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e-93

   1. Initial program 71.9%

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

      1. *-commutative 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in z around inf 71.8%

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

   6. Taylor expanded in t around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-frac-neg 75.5%

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

      3. sub-neg 75.5%

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

      4. +-commutative 75.5%

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

      5. distribute-neg-in 75.5%

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

      6. remove-double-neg 75.5%

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

      7. unsub-neg 75.5%

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

   8. Simplified 75.5%

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

   if -1.1499999999999999e-93 < z < 7.0000000000000001e-12

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.0%

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

   if 7.0000000000000001e-12 < z

   1. Initial program 77.0%

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

      1. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 77.0%

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

   6. Taylor expanded in x around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. mul-1-neg 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93} \lor \neg \left(z \leq 0.001\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-93) (not (<= z 0.001))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-93) || !(z <= 0.001)) {
		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 <= (-1.15d-93)) .or. (.not. (z <= 0.001d0))) 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 <= -1.15e-93) || !(z <= 0.001)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-93) or not (z <= 0.001):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-93) || !(z <= 0.001))
		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 <= -1.15e-93) || ~((z <= 0.001)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-93], N[Not[LessEqual[z, 0.001]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e-93 or 1e-3 < z

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in z around inf 55.4%

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

   if -1.1499999999999999e-93 < z < 1e-3

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 65.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-93} \lor \neg \left(z \leq 0.001\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.1% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.7%

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

   1. *-commutative 84.7%

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

3. Simplified 84.7%

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

5. Taylor expanded in z around 0 36.0%

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

Developer Target 1: 97.5% 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 2024136 
(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))))