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

Average Error: 10.9 → 2.5

Time: 15.1s

Precision: binary64

Cost: 8584

Math

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

↓

\[\begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y}{\frac{t_1}{z}}\\ t_3 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-312}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, y, -x\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;t_3 \leq 10^{+276}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

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 (- (* z a) t))
        (t_2 (/ y (/ t_1 z)))
        (t_3 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 -1e-312)
       (/ (fma z y (- x)) t_1)
       (if (<= t_3 0.0)
         (/ (/ (- (* y z) x) a) z)
         (if (<= t_3 1e+276) t_3 (if (<= t_3 INFINITY) t_2 (/ y a))))))))

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 = (z * a) - t;
	double t_2 = y / (t_1 / z);
	double t_3 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= -1e-312) {
		tmp = fma(z, y, -x) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_3 <= 1e+276) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	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(Float64(z * a) - t)
	t_2 = Float64(y / Float64(t_1 / z))
	t_3 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= -1e-312)
		tmp = Float64(fma(z, y, Float64(-x)) / t_1);
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y * z) - x) / a) / z);
	elseif (t_3 <= 1e+276)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	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[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, -1e-312], N[(N[(z * y + (-x)), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, 1e+276], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]]

Target

Original	10.9
Target	1.7
Herbie	2.5

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

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0 or 1.0000000000000001e276 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 55.1

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

   2. Simplified 55.1

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

      [Start] 55.1	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 55.1	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 55.1	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 55.1	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 55.1	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 55.1	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 55.1	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 55.1	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 55.1	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 55.1	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 55.1	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 55.1	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 55.1	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      times-frac [=>] 55.1	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 55.1	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 55.1	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 55.1	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in y around inf 61.3

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

   4. Simplified 6.5

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

      [Start] 61.3	\[ \frac{y \cdot z}{a \cdot z - t} \]
      associate-/l* [=>] 6.5	\[ \color{blue}{\frac{y}{\frac{a \cdot z - t}{z}}} \]

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -9.9999999999847e-313

   1. Initial program 0.2

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

   2. Simplified 0.2

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

      [Start] 0.2	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 0.2	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 0.2	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 0.2	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 0.2	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 0.2	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 0.2	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 0.2	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 0.2	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 0.2	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 0.2	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 0.2	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 0.2	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      times-frac [=>] 0.2	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 0.2	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 0.2	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 0.2	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Applied egg-rr 0.2

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

   if -9.9999999999847e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 25.8

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

   2. Simplified 25.8

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

      [Start] 25.8	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 25.8	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 25.8	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 25.8	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 25.8	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 25.8	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 25.8	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 25.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 25.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 25.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 25.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 25.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 25.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      times-frac [=>] 25.8	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 25.8	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 25.8	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 25.8	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in a around inf 41.8

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

   4. Simplified 41.8

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

      [Start] 41.8	\[ \frac{y \cdot z - x}{a \cdot z} \]
      *-commutative [=>] 41.8	\[ \frac{\color{blue}{z \cdot y} - x}{a \cdot z} \]

   5. Applied egg-rr 13.2

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

   6. Applied egg-rr 13.2

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.0000000000000001e276

   1. Initial program 0.2

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

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

   1. Initial program 64.0

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

   2. Simplified 64.0

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

      [Start] 64.0	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 64.0	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 64.0	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 64.0	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 64.0	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 64.0	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 64.0	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 64.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 64.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 64.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 64.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 64.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 64.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      times-frac [=>] 64.0	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 64.0	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 64.0	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 64.0	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in z around inf 0.0

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

4. Final simplification 2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-312}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, y, -x\right)}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+276}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternatives

Alternative 1
Error	2.5
Cost	4436

\[\begin{array}{l} t_1 := \frac{y}{\frac{z \cdot a - t}{z}}\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-312}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;t_2 \leq 10^{+276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 2
Error	18.2
Cost	844

\[\begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -650:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 6400:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	20.7
Cost	844

\[\begin{array}{l} t_1 := z \cdot a - t\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{\frac{t_1}{z}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-200}:\\ \;\;\;\;\frac{-x}{t_1}\\ \mathbf{elif}\;z \leq 0.94:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 4
Error	19.3
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+78} \lor \neg \left(z \leq 32\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 5
Error	24.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+85}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6
Error	31.9
Cost	648

\[\begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+205}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 1.4:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7
Error	29.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 0.82:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8
Error	42.5
Cost	192

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

Reproduce

herbie shell --seed 2023073 
(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))))