Average Error: 17.0 → 13.2
Time: 17.7s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.200885699998733444989436015220153683456 \cdot 10^{-71}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;y \le 6.270483262385894464092382197729043283474 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{\sqrt[3]{\frac{b \cdot y}{t}} \cdot \left(\sqrt[3]{\frac{b \cdot y}{t}} \cdot \sqrt[3]{\frac{b \cdot y}{t}}\right) + \left(1 + a\right)} \cdot \left(\frac{z \cdot y}{t} + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.200885699998733444989436015220153683456 \cdot 10^{-71}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\

\mathbf{elif}\;y \le 6.270483262385894464092382197729043283474 \cdot 10^{-82}:\\
\;\;\;\;\frac{1}{\sqrt[3]{\frac{b \cdot y}{t}} \cdot \left(\sqrt[3]{\frac{b \cdot y}{t}} \cdot \sqrt[3]{\frac{b \cdot y}{t}}\right) + \left(1 + a\right)} \cdot \left(\frac{z \cdot y}{t} + x\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r33941186 = x;
        double r33941187 = y;
        double r33941188 = z;
        double r33941189 = r33941187 * r33941188;
        double r33941190 = t;
        double r33941191 = r33941189 / r33941190;
        double r33941192 = r33941186 + r33941191;
        double r33941193 = a;
        double r33941194 = 1.0;
        double r33941195 = r33941193 + r33941194;
        double r33941196 = b;
        double r33941197 = r33941187 * r33941196;
        double r33941198 = r33941197 / r33941190;
        double r33941199 = r33941195 + r33941198;
        double r33941200 = r33941192 / r33941199;
        return r33941200;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r33941201 = y;
        double r33941202 = -5.2008856999987334e-71;
        bool r33941203 = r33941201 <= r33941202;
        double r33941204 = x;
        double r33941205 = t;
        double r33941206 = z;
        double r33941207 = r33941205 / r33941206;
        double r33941208 = r33941201 / r33941207;
        double r33941209 = r33941204 + r33941208;
        double r33941210 = 1.0;
        double r33941211 = a;
        double r33941212 = r33941210 + r33941211;
        double r33941213 = b;
        double r33941214 = r33941205 / r33941213;
        double r33941215 = r33941201 / r33941214;
        double r33941216 = r33941212 + r33941215;
        double r33941217 = r33941209 / r33941216;
        double r33941218 = 6.270483262385894e-82;
        bool r33941219 = r33941201 <= r33941218;
        double r33941220 = 1.0;
        double r33941221 = r33941213 * r33941201;
        double r33941222 = r33941221 / r33941205;
        double r33941223 = cbrt(r33941222);
        double r33941224 = r33941223 * r33941223;
        double r33941225 = r33941223 * r33941224;
        double r33941226 = r33941225 + r33941212;
        double r33941227 = r33941220 / r33941226;
        double r33941228 = r33941206 * r33941201;
        double r33941229 = r33941228 / r33941205;
        double r33941230 = r33941229 + r33941204;
        double r33941231 = r33941227 * r33941230;
        double r33941232 = r33941219 ? r33941231 : r33941217;
        double r33941233 = r33941203 ? r33941217 : r33941232;
        return r33941233;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original17.0
Target13.5
Herbie13.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.2008856999987334e-71 or 6.270483262385894e-82 < y

    1. Initial program 25.5

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    2. Using strategy rm

    3. Applied div-inv25.5

      \[\leadsto \color{blue}{\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}}\]
    4. Using strategy rm

    5. Applied associate-*r/25.5

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

    6. Simplified23.1

      \[\leadsto \frac{\color{blue}{x + \frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    7. Using strategy rm

    8. Applied associate-/l*19.2

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

    if -5.2008856999987334e-71 < y < 6.270483262385894e-82

    1. Initial program 2.9

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    2. Using strategy rm

    3. Applied div-inv3.0

      \[\leadsto \color{blue}{\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}}\]
    4. Using strategy rm

    5. Applied add-cube-cbrt3.1

      \[\leadsto \left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \color{blue}{\left(\sqrt[3]{\frac{y \cdot b}{t}} \cdot \sqrt[3]{\frac{y \cdot b}{t}}\right) \cdot \sqrt[3]{\frac{y \cdot b}{t}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification13.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.200885699998733444989436015220153683456 \cdot 10^{-71}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;y \le 6.270483262385894464092382197729043283474 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{\sqrt[3]{\frac{b \cdot y}{t}} \cdot \left(\sqrt[3]{\frac{b \cdot y}{t}} \cdot \sqrt[3]{\frac{b \cdot y}{t}}\right) + \left(1 + a\right)} \cdot \left(\frac{z \cdot y}{t} + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(1 + a\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))