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

↓

\[\begin{array}{l} \mathbf{if}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -1.571841906786876071087337949480536432104 \cdot 10^{-148}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1}{\frac{a - t}{t - z}}, y + x\right)\\ \mathbf{elif}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 0.0 \lor \neg \left(\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 1.838881673180893407071567641483887773699 \cdot 10^{307}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -1.571841906786876071087337949480536432104 \cdot 10^{-148}:\\
\;\;\;\;\mathsf{fma}\left(y, \frac{1}{\frac{a - t}{t - z}}, y + x\right)\\

\mathbf{elif}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 0.0 \lor \neg \left(\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 1.838881673180893407071567641483887773699 \cdot 10^{307}\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r395189 = x;
        double r395190 = y;
        double r395191 = r395189 + r395190;
        double r395192 = z;
        double r395193 = t;
        double r395194 = r395192 - r395193;
        double r395195 = r395194 * r395190;
        double r395196 = a;
        double r395197 = r395196 - r395193;
        double r395198 = r395195 / r395197;
        double r395199 = r395191 - r395198;
        return r395199;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r395200 = y;
        double r395201 = x;
        double r395202 = r395200 + r395201;
        double r395203 = z;
        double r395204 = t;
        double r395205 = r395203 - r395204;
        double r395206 = r395205 * r395200;
        double r395207 = a;
        double r395208 = r395207 - r395204;
        double r395209 = r395206 / r395208;
        double r395210 = r395202 - r395209;
        double r395211 = -1.571841906786876e-148;
        bool r395212 = r395210 <= r395211;
        double r395213 = 1.0;
        double r395214 = r395204 - r395203;
        double r395215 = r395208 / r395214;
        double r395216 = r395213 / r395215;
        double r395217 = fma(r395200, r395216, r395202);
        double r395218 = 0.0;
        bool r395219 = r395210 <= r395218;
        double r395220 = 1.8388816731808934e+307;
        bool r395221 = r395210 <= r395220;
        double r395222 = !r395221;
        bool r395223 = r395219 || r395222;
        double r395224 = r395203 / r395204;
        double r395225 = fma(r395224, r395200, r395201);
        double r395226 = r395223 ? r395225 : r395210;
        double r395227 = r395212 ? r395217 : r395226;
        return r395227;
}

Original	16.7
Target	8.6
Herbie	8.2

Derivation

Split input into 3 regimes
if (- (+ x y) (/ (* (- z t) y) (- a t))) < -1.571841906786876e-148
1. Initial program 13.4
  \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
2. Simplified7.7
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - z}{a - t}, y + x\right)}\]
3. Using strategy rm
4. Applied clear-num7.7
  \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{1}{\frac{a - t}{t - z}}}, y + x\right)\]
if -1.571841906786876e-148 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 0.0 or 1.8388816731808934e+307 < (- (+ x y) (/ (* (- z t) y) (- a t)))
1. Initial program 55.0
  \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
2. Simplified39.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - z}{a - t}, y + x\right)}\]
3. Taylor expanded around inf 29.3
  \[\leadsto \color{blue}{\frac{z \cdot y}{t} + x}\]
4. Simplified22.6
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}\]
if 0.0 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 1.8388816731808934e+307
1. Initial program 1.4
  \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
Recombined 3 regimes into one program.
Final simplification8.2
\[\leadsto \begin{array}{l} \mathbf{if}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -1.571841906786876071087337949480536432104 \cdot 10^{-148}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1}{\frac{a - t}{t - z}}, y + x\right)\\ \mathbf{elif}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 0.0 \lor \neg \left(\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 1.838881673180893407071567641483887773699 \cdot 10^{307}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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

Error

Target

Derivation

`if (- (+ x y) (/ (* (- z t) y) (- a t))) < -1.571841906786876e-148`

`if -1.571841906786876e-148 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 0.0 or 1.8388816731808934e+307 < (- (+ x y) (/ (* (- z t) y) (- a t)))`

`if 0.0 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 1.8388816731808934e+307`

Reproduce