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

Average Accuracy: 76.6% → 87.9%

Time: 18.3s

Precision: binary64

Cost: 10128

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ t_3 := y \cdot z - x\\ t_4 := \frac{t_3}{\mathsf{fma}\left(z, a, -t\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-322}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t_3}{a} \cdot \frac{1}{z}\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a (/ t z))))
        (t_2 (/ (- x (* y z)) (- t (* z a))))
        (t_3 (- (* y z) x))
        (t_4 (/ t_3 (fma z a (- t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-322)
       t_4
       (if (<= t_2 0.0)
         (* (/ t_3 a) (/ 1.0 z))
         (if (<= t_2 4e+266) t_4 t_1))))))

C

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

↓

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 t_3 = (y * z) - x;
	double t_4 = t_3 / fma(z, a, -t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-322) {
		tmp = t_4;
	} else if (t_2 <= 0.0) {
		tmp = (t_3 / a) * (1.0 / z);
	} else if (t_2 <= 4e+266) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

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

↓

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)))
	t_3 = Float64(Float64(y * z) - x)
	t_4 = Float64(t_3 / fma(z, a, Float64(-t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-322)
		tmp = t_4;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t_3 / a) * Float64(1.0 / z));
	elseif (t_2 <= 4e+266)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

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

↓

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]}, Block[{t$95$3 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(z * a + (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-322], t$95$4, If[LessEqual[t$95$2, 0.0], N[(N[(t$95$3 / a), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+266], t$95$4, t$95$1]]]]]]]]

Target

Original	76.6%
Target	89.2%
Herbie	87.9%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0 or 4.0000000000000001e266 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 4.2%

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

   2. Simplified 4.2%

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

      [Start] 4.2	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 4.2	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 4.2	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 4.2	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 4.2	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 4.2	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 4.2	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 4.2	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 4.2	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 4.2	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 4.2	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 4.2	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 4.2	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 4.2	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 4.2	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 4.2	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 4.2	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Applied egg-rr 26.1%

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

      [Start] 4.2	\[ \frac{y \cdot z - x}{z \cdot a - t} \]
      div-sub [=>] 4.2	\[ \color{blue}{\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}} \]
      associate-/l* [=>] 26.1	\[ \color{blue}{\frac{y}{\frac{z \cdot a - t}{z}}} - \frac{x}{z \cdot a - t} \]

   4. Taylor expanded in z around 0 44.6%

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

   5. Simplified 44.6%

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

      [Start] 44.6	\[ \frac{y}{a + -1 \cdot \frac{t}{z}} - \frac{x}{z \cdot a - t} \]
      neg-mul-1 [<=] 44.6	\[ \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} - \frac{x}{z \cdot a - t} \]
      sub-neg [<=] 44.6	\[ \frac{y}{\color{blue}{a - \frac{t}{z}}} - \frac{x}{z \cdot a - t} \]

   6. Taylor expanded in y around inf 45.0%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.97626e-322 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.0000000000000001e266

   1. Initial program 99.7%

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

   2. Simplified 99.7%

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

      [Start] 99.7	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 99.7	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 99.7	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 99.7	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 99.7	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 99.7	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 99.7	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 99.7	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 99.7	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 99.7	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 99.7	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 99.7	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 99.7	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 99.7	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 99.7	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 99.7	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 99.7	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Applied egg-rr 99.7%

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

      [Start] 99.7	\[ \frac{y \cdot z - x}{z \cdot a - t} \]
      fma-neg [=>] 99.7	\[ \frac{y \cdot z - x}{\color{blue}{\mathsf{fma}\left(z, a, -t\right)}} \]

   if -1.97626e-322 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 61.8%

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

   2. Simplified 61.8%

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

      [Start] 61.8	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 61.8	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 61.8	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 61.8	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 61.8	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 61.8	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 61.8	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 61.8	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 61.8	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 61.8	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 61.8	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 61.8	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 61.8	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 61.8	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 61.8	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 61.8	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 61.8	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in a around inf 42.4%

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

   4. Simplified 42.4%

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

      [Start] 42.4	\[ \frac{y \cdot z - x}{a \cdot z} \]
      *-commutative [=>] 42.4	\[ \frac{\color{blue}{z \cdot y} - x}{a \cdot z} \]

   5. Applied egg-rr 85.2%

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

      [Start] 42.4	\[ \frac{z \cdot y - x}{a \cdot z} \]
      associate-/r* [=>] 85.3	\[ \color{blue}{\frac{\frac{z \cdot y - x}{a}}{z}} \]
      div-inv [=>] 85.2	\[ \color{blue}{\frac{z \cdot y - x}{a} \cdot \frac{1}{z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-322}:\\ \;\;\;\;\frac{y \cdot z - x}{\mathsf{fma}\left(z, a, -t\right)}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y \cdot z - x}{a} \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 4 \cdot 10^{+266}:\\ \;\;\;\;\frac{y \cdot z - x}{\mathsf{fma}\left(z, a, -t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	87.9%
Cost	3792

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-322}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{y \cdot z - x}{a} \cdot \frac{1}{z}\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	87.7%
Cost	3792

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ t_2 := z \cdot a - t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{\frac{1}{z} \cdot t_2} - \frac{x}{t_2}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-322}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{y \cdot z - x}{a} \cdot \frac{1}{z}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+266}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternative 3
Accuracy	38.5%
Cost	1440

\[\begin{array}{l} t_1 := \frac{z}{\frac{t}{-y}}\\ \mathbf{if}\;t \leq -3.85 \cdot 10^{+248}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-169}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-191}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;t \leq 360000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+262}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 4
Accuracy	65.2%
Cost	1108

\[\begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.35 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	46.4%
Cost	1044

\[\begin{array}{l} t_1 := \frac{\frac{-x}{a}}{z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6
Accuracy	46.5%
Cost	1044

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7
Accuracy	58.0%
Cost	977

\[\begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -1260 \lor \neg \left(z \leq 4 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 8
Accuracy	63.9%
Cost	977

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -3.85 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-45} \lor \neg \left(z \leq 3.7 \cdot 10^{-31}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 9
Accuracy	48.6%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10
Accuracy	31.6%
Cost	192

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

Reproduce

herbie shell --seed 2023157 
(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))))