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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -2.72829081956777889 \cdot 10^{-39} \lor \neg \left(a \le 8.58934647090694211 \cdot 10^{-217}\right):\\ \;\;\;\;\frac{y - z}{a - z} \cdot \left(t - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \end{array}\]

x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}

↓

\begin{array}{l}
\mathbf{if}\;a \le -2.72829081956777889 \cdot 10^{-39} \lor \neg \left(a \le 8.58934647090694211 \cdot 10^{-217}\right):\\
\;\;\;\;\frac{y - z}{a - z} \cdot \left(t - x\right) + x\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r586589 = x;
        double r586590 = y;
        double r586591 = z;
        double r586592 = r586590 - r586591;
        double r586593 = t;
        double r586594 = r586593 - r586589;
        double r586595 = r586592 * r586594;
        double r586596 = a;
        double r586597 = r586596 - r586591;
        double r586598 = r586595 / r586597;
        double r586599 = r586589 + r586598;
        return r586599;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r586600 = a;
        double r586601 = -2.728290819567779e-39;
        bool r586602 = r586600 <= r586601;
        double r586603 = 8.589346470906942e-217;
        bool r586604 = r586600 <= r586603;
        double r586605 = !r586604;
        bool r586606 = r586602 || r586605;
        double r586607 = y;
        double r586608 = z;
        double r586609 = r586607 - r586608;
        double r586610 = r586600 - r586608;
        double r586611 = r586609 / r586610;
        double r586612 = t;
        double r586613 = x;
        double r586614 = r586612 - r586613;
        double r586615 = r586611 * r586614;
        double r586616 = r586615 + r586613;
        double r586617 = r586613 / r586608;
        double r586618 = r586612 / r586608;
        double r586619 = r586617 - r586618;
        double r586620 = fma(r586607, r586619, r586612);
        double r586621 = r586606 ? r586616 : r586620;
        return r586621;
}

Original	24.3
Target	11.8
Herbie	10.4

Derivation

Split input into 2 regimes
if a < -2.728290819567779e-39 or 8.589346470906942e-217 < a
1. Initial program 23.0
  \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
2. Simplified9.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)}\]
3. Using strategy rm
4. Applied fma-udef9.1
  \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right) + x}\]
if -2.728290819567779e-39 < a < 8.589346470906942e-217
1. Initial program 28.1
  \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
2. Simplified19.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)}\]
3. Taylor expanded around inf 16.1
  \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}}\]
4. Simplified14.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)}\]
Recombined 2 regimes into one program.
Final simplification10.4
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.72829081956777889 \cdot 10^{-39} \lor \neg \left(a \le 8.58934647090694211 \cdot 10^{-217}\right):\\ \;\;\;\;\frac{y - z}{a - z} \cdot \left(t - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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

Error

Target

Derivation

`if a < -2.728290819567779e-39 or 8.589346470906942e-217 < a`

`if -2.728290819567779e-39 < a < 8.589346470906942e-217`

Reproduce