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

Percentage Accurate: 84.8% → 92.3%

Time: 9.2s

Alternatives: 8

Speedup: 0.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% 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: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-312}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a (/ t z)))) (t_2 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-312)
       t_2
       (if (<= t_2 0.0) (/ (- y (/ x z)) a) (if (<= t_2 2e+300) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - (t / z));
	double t_2 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-312) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_2 <= 2e+300) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - (t / z));
	double t_2 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-312) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_2 <= 2e+300) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - (t / z))
	t_2 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-312:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (y - (x / z)) / a
	elif t_2 <= 2e+300:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - Float64(t / z)))
	t_2 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-312)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (t_2 <= 2e+300)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - (t / z));
	t_2 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-312)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (y - (x / z)) / a;
	elseif (t_2 <= 2e+300)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-312], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$2, 2e+300], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0 or 2.0000000000000001e300 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 28.8%

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

      1. *-commutative 28.8%

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

   3. Simplified 28.8%

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

      1. div-sub 28.8%

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

      2. div-inv 28.8%

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

      3. fma-neg 28.8%

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

   5. Applied egg-rr 28.8%

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

   6. Taylor expanded in x around 0 12.2%

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

      1. associate-*r/ 12.2%

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

      2. mul-1-neg 12.2%

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

      3. distribute-rgt-neg-out 12.2%

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

      4. *-commutative 12.2%

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

      5. associate-/l* 66.5%

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

   8. Simplified 66.5%

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

   9. Taylor expanded in t around 0 83.1%

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

       1. mul-1-neg 83.1%

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

       2. unsub-neg 83.1%

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

   11. Simplified 83.1%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.0000000000022e-312 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2.0000000000000001e300

   1. Initial program 99.6%

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

   if -5.0000000000022e-312 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 45.0%

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

      1. *-commutative 45.0%

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

   3. Simplified 45.0%

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

      1. div-sub 45.0%

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

      2. div-inv 45.0%

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

      3. fma-neg 45.0%

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

   5. Applied egg-rr 45.0%

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

   6. Taylor expanded in t around 0 65.4%

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

      1. distribute-lft-out-- 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-/r* 84.6%

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

      4. div-sub 84.6%

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

      5. mul-1-neg 84.6%

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

   8. Simplified 84.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-312}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternative 2: 44.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-244}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+264}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e-59)
   (/ x t)
   (if (<= t -3e-244)
     (/ y a)
     (if (<= t 6.8e-157)
       (/ (- x) (* z a))
       (if (<= t 4.8e-51)
         (/ y a)
         (if (<= t 5e+194)
           (/ x t)
           (if (<= t 3.1e+264) (- (* z (/ y t))) (/ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e-59) {
		tmp = x / t;
	} else if (t <= -3e-244) {
		tmp = y / a;
	} else if (t <= 6.8e-157) {
		tmp = -x / (z * a);
	} else if (t <= 4.8e-51) {
		tmp = y / a;
	} else if (t <= 5e+194) {
		tmp = x / t;
	} else if (t <= 3.1e+264) {
		tmp = -(z * (y / t));
	} 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 (t <= (-2.8d-59)) then
        tmp = x / t
    else if (t <= (-3d-244)) then
        tmp = y / a
    else if (t <= 6.8d-157) then
        tmp = -x / (z * a)
    else if (t <= 4.8d-51) then
        tmp = y / a
    else if (t <= 5d+194) then
        tmp = x / t
    else if (t <= 3.1d+264) then
        tmp = -(z * (y / t))
    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 (t <= -2.8e-59) {
		tmp = x / t;
	} else if (t <= -3e-244) {
		tmp = y / a;
	} else if (t <= 6.8e-157) {
		tmp = -x / (z * a);
	} else if (t <= 4.8e-51) {
		tmp = y / a;
	} else if (t <= 5e+194) {
		tmp = x / t;
	} else if (t <= 3.1e+264) {
		tmp = -(z * (y / t));
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e-59:
		tmp = x / t
	elif t <= -3e-244:
		tmp = y / a
	elif t <= 6.8e-157:
		tmp = -x / (z * a)
	elif t <= 4.8e-51:
		tmp = y / a
	elif t <= 5e+194:
		tmp = x / t
	elif t <= 3.1e+264:
		tmp = -(z * (y / t))
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e-59)
		tmp = Float64(x / t);
	elseif (t <= -3e-244)
		tmp = Float64(y / a);
	elseif (t <= 6.8e-157)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (t <= 4.8e-51)
		tmp = Float64(y / a);
	elseif (t <= 5e+194)
		tmp = Float64(x / t);
	elseif (t <= 3.1e+264)
		tmp = Float64(-Float64(z * Float64(y / t)));
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e-59)
		tmp = x / t;
	elseif (t <= -3e-244)
		tmp = y / a;
	elseif (t <= 6.8e-157)
		tmp = -x / (z * a);
	elseif (t <= 4.8e-51)
		tmp = y / a;
	elseif (t <= 5e+194)
		tmp = x / t;
	elseif (t <= 3.1e+264)
		tmp = -(z * (y / t));
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e-59], N[(x / t), $MachinePrecision], If[LessEqual[t, -3e-244], N[(y / a), $MachinePrecision], If[LessEqual[t, 6.8e-157], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-51], N[(y / a), $MachinePrecision], If[LessEqual[t, 5e+194], N[(x / t), $MachinePrecision], If[LessEqual[t, 3.1e+264], (-N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), N[(x / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.79999999999999981e-59 or 4.8e-51 < t < 4.99999999999999989e194 or 3.09999999999999981e264 < t

   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. Taylor expanded in z around 0 50.0%

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

   if -2.79999999999999981e-59 < t < -3.0000000000000001e-244 or 6.79999999999999955e-157 < t < 4.8e-51

   1. Initial program 79.0%

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

      1. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in z around inf 60.8%

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

   if -3.0000000000000001e-244 < t < 6.79999999999999955e-157

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. neg-mul-1 75.5%

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

      3. neg-sub0 75.5%

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

      4. sub-neg 75.5%

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

      5. distribute-rgt-neg-out 75.5%

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

      6. +-commutative 75.5%

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

      7. associate--r+ 75.5%

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

      8. neg-sub0 75.5%

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

      9. distribute-rgt-neg-out 75.5%

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

      10. remove-double-neg 75.5%

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

      11. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around 0 59.2%

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

      1. neg-mul-1 59.2%

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

   9. Simplified 59.2%

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

   if 4.99999999999999989e194 < t < 3.09999999999999981e264

   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. Taylor expanded in z around 0 90.8%

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

      1. fma-def 90.8%

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

      2. distribute-lft-out-- 90.8%

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

      3. associate-/l* 90.8%

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

      4. unpow2 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in z around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-*l/ 73.9%

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

      3. unpow2 73.9%

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

      4. distribute-rgt-neg-out 73.9%

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

      5. unpow2 73.9%

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

      6. associate-*l/ 73.9%

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

      7. associate-/l* 73.9%

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

      8. unpow2 73.9%

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

   9. Simplified 73.9%

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

   10. Taylor expanded in y around inf 73.9%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-244}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+264}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 3: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{+93}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+17} \lor \neg \left(z \leq 1.5 \cdot 10^{+77}\right) \land z \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.15e+93)
   (/ y a)
   (if (or (<= z 5.3e+17) (and (not (<= z 1.5e+77)) (<= z 5.2e+143)))
     (/ x (- t (* z a)))
     (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.15e+93) {
		tmp = y / a;
	} else if ((z <= 5.3e+17) || (!(z <= 1.5e+77) && (z <= 5.2e+143))) {
		tmp = x / (t - (z * a));
	} 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 <= (-4.15d+93)) then
        tmp = y / a
    else if ((z <= 5.3d+17) .or. (.not. (z <= 1.5d+77)) .and. (z <= 5.2d+143)) then
        tmp = x / (t - (z * a))
    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 <= -4.15e+93) {
		tmp = y / a;
	} else if ((z <= 5.3e+17) || (!(z <= 1.5e+77) && (z <= 5.2e+143))) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.15e+93:
		tmp = y / a
	elif (z <= 5.3e+17) or (not (z <= 1.5e+77) and (z <= 5.2e+143)):
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.15e+93)
		tmp = Float64(y / a);
	elseif ((z <= 5.3e+17) || (!(z <= 1.5e+77) && (z <= 5.2e+143)))
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.15e+93)
		tmp = y / a;
	elseif ((z <= 5.3e+17) || (~((z <= 1.5e+77)) && (z <= 5.2e+143)))
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.15e+93], N[(y / a), $MachinePrecision], If[Or[LessEqual[z, 5.3e+17], And[N[Not[LessEqual[z, 1.5e+77]], $MachinePrecision], LessEqual[z, 5.2e+143]]], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1499999999999999e93 or 5.3e17 < z < 1.4999999999999999e77 or 5.1999999999999998e143 < z

   1. Initial program 54.7%

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

      1. *-commutative 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in z around inf 61.3%

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

   if -4.1499999999999999e93 < z < 5.3e17 or 1.4999999999999999e77 < z < 5.1999999999999998e143

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around inf 71.2%

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

      1. *-commutative 71.2%

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

   6. Simplified 71.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{+93}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+17} \lor \neg \left(z \leq 1.5 \cdot 10^{+77}\right) \land z \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 4: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+45)
   (/ y a)
   (if (<= z 3.1e+15)
     (/ x t)
     (if (<= z 5.9e+84)
       (/ y a)
       (if (<= z 9.8e+123) (- (* z (/ y t))) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+45) {
		tmp = y / a;
	} else if (z <= 3.1e+15) {
		tmp = x / t;
	} else if (z <= 5.9e+84) {
		tmp = y / a;
	} else if (z <= 9.8e+123) {
		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 <= (-1.5d+45)) then
        tmp = y / a
    else if (z <= 3.1d+15) then
        tmp = x / t
    else if (z <= 5.9d+84) then
        tmp = y / a
    else if (z <= 9.8d+123) 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 <= -1.5e+45) {
		tmp = y / a;
	} else if (z <= 3.1e+15) {
		tmp = x / t;
	} else if (z <= 5.9e+84) {
		tmp = y / a;
	} else if (z <= 9.8e+123) {
		tmp = -(z * (y / t));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+45:
		tmp = y / a
	elif z <= 3.1e+15:
		tmp = x / t
	elif z <= 5.9e+84:
		tmp = y / a
	elif z <= 9.8e+123:
		tmp = -(z * (y / t))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+45)
		tmp = Float64(y / a);
	elseif (z <= 3.1e+15)
		tmp = Float64(x / t);
	elseif (z <= 5.9e+84)
		tmp = Float64(y / a);
	elseif (z <= 9.8e+123)
		tmp = Float64(-Float64(z * Float64(y / t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+45)
		tmp = y / a;
	elseif (z <= 3.1e+15)
		tmp = x / t;
	elseif (z <= 5.9e+84)
		tmp = y / a;
	elseif (z <= 9.8e+123)
		tmp = -(z * (y / t));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+45], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.1e+15], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.9e+84], N[(y / a), $MachinePrecision], If[LessEqual[z, 9.8e+123], (-N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000005e45 or 3.1e15 < z < 5.89999999999999984e84 or 9.79999999999999952e123 < z

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in z around inf 55.4%

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

   if -1.50000000000000005e45 < z < 3.1e15

   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. Taylor expanded in z around 0 49.3%

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

   if 5.89999999999999984e84 < z < 9.79999999999999952e123

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 63.3%

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

      1. fma-def 63.3%

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

      2. distribute-lft-out-- 63.3%

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

      3. associate-/l* 63.3%

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

      4. unpow2 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in z around inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. associate-*l/ 63.3%

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

      3. unpow2 63.3%

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

      4. distribute-rgt-neg-out 63.3%

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

      5. unpow2 63.3%

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

      6. associate-*l/ 63.3%

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

      7. associate-/l* 63.3%

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

      8. unpow2 63.3%

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

   9. Simplified 63.3%

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

   10. Taylor expanded in y around inf 63.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 71.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85} \lor \neg \left(y \leq 0.000105\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.1e+85) (not (<= y 0.000105)))
   (/ y (- a (/ t z)))
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e+85) || !(y <= 0.000105)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.1d+85)) .or. (.not. (y <= 0.000105d0))) then
        tmp = y / (a - (t / z))
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e+85) || !(y <= 0.000105)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.1e+85) or not (y <= 0.000105):
		tmp = y / (a - (t / z))
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.1e+85) || !(y <= 0.000105))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.1e+85) || ~((y <= 0.000105)))
		tmp = y / (a - (t / z));
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.1e+85], N[Not[LessEqual[y, 0.000105]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e85 or 1.05e-4 < y

   1. Initial program 68.7%

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

      1. *-commutative 68.7%

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

   3. Simplified 68.7%

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

      1. div-sub 68.7%

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

      2. div-inv 68.7%

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

      3. fma-neg 68.7%

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

   5. Applied egg-rr 68.7%

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

   6. Taylor expanded in x around 0 47.4%

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

      1. associate-*r/ 47.4%

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

      2. mul-1-neg 47.4%

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

      3. distribute-rgt-neg-out 47.4%

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

      4. *-commutative 47.4%

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

      5. associate-/l* 61.1%

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

   8. Simplified 61.1%

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

   9. Taylor expanded in t around 0 72.3%

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

       1. mul-1-neg 72.3%

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

       2. unsub-neg 72.3%

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

   11. Simplified 72.3%

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

   if -2.1000000000000001e85 < y < 1.05e-4

   1. Initial program 92.2%

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

      1. *-commutative 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 75.1%

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

      1. *-commutative 75.1%

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

   6. Simplified 75.1%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+85} \lor \neg \left(y \leq 0.000105\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 6: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+45}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.06e+45)
   (/ (- y (/ x z)) a)
   (if (<= z 1.15e-8) (/ 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 <= -1.06e+45) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 1.15e-8) {
		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 <= (-1.06d+45)) then
        tmp = (y - (x / z)) / a
    else if (z <= 1.15d-8) 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 <= -1.06e+45) {
		tmp = (y - (x / z)) / a;
	} else if (z <= 1.15e-8) {
		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 <= -1.06e+45:
		tmp = (y - (x / z)) / a
	elif z <= 1.15e-8:
		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 <= -1.06e+45)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (z <= 1.15e-8)
		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 <= -1.06e+45)
		tmp = (y - (x / z)) / a;
	elseif (z <= 1.15e-8)
		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, -1.06e+45], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.15e-8], 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 < -1.06e45

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

      1. div-sub 61.5%

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

      2. div-inv 61.4%

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

      3. fma-neg 61.4%

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

   5. Applied egg-rr 61.4%

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

   6. Taylor expanded in t around 0 69.5%

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

      1. distribute-lft-out-- 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-/r* 75.1%

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

      4. div-sub 75.1%

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

      5. mul-1-neg 75.1%

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

   8. Simplified 75.1%

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

   if -1.06e45 < z < 1.15e-8

   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. Taylor expanded in x around inf 76.3%

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

      1. *-commutative 76.3%

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

   6. Simplified 76.3%

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

   if 1.15e-8 < z

   1. Initial program 70.9%

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

      1. *-commutative 70.9%

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

   3. Simplified 70.9%

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

      1. div-sub 70.9%

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

      2. div-inv 70.8%

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

      3. fma-neg 70.8%

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

   5. Applied egg-rr 70.8%

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

   6. Taylor expanded in x around 0 45.9%

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

      1. associate-*r/ 45.9%

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

      2. mul-1-neg 45.9%

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

      3. distribute-rgt-neg-out 45.9%

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

      4. *-commutative 45.9%

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

      5. associate-/l* 58.5%

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

   8. Simplified 58.5%

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

   9. Taylor expanded in t around 0 70.6%

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

       1. mul-1-neg 70.6%

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

       2. unsub-neg 70.6%

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

   11. Simplified 70.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+45}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternative 7: 55.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+44) (/ y a) (if (<= z 1.52e+16) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+44) {
		tmp = y / a;
	} else if (z <= 1.52e+16) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.2d+44)) then
        tmp = y / a
    else if (z <= 1.52d+16) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+44) {
		tmp = y / a;
	} else if (z <= 1.52e+16) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e+44:
		tmp = y / a
	elif z <= 1.52e+16:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+44)
		tmp = Float64(y / a);
	elseif (z <= 1.52e+16)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e+44)
		tmp = y / a;
	elseif (z <= 1.52e+16)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+44], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.52e+16], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999991e44 or 1.52e16 < z

   1. Initial program 63.7%

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

      1. *-commutative 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around inf 52.6%

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

   if -6.19999999999999991e44 < z < 1.52e16

   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. Taylor expanded in z around 0 49.3%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 35.4% 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 83.1%

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

   1. *-commutative 83.1%

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

3. Simplified 83.1%

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

4. Taylor expanded in z around 0 34.4%

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

5. Final simplification 34.4%

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

Developer target: 97.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

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

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