\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

↓

\[\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\]

\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}

↓

\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r417500 = x;
        double r417501 = y;
        double r417502 = 2.0;
        double r417503 = z;
        double r417504 = t;
        double r417505 = a;
        double r417506 = r417504 + r417505;
        double r417507 = sqrt(r417506);
        double r417508 = r417503 * r417507;
        double r417509 = r417508 / r417504;
        double r417510 = b;
        double r417511 = c;
        double r417512 = r417510 - r417511;
        double r417513 = 5.0;
        double r417514 = 6.0;
        double r417515 = r417513 / r417514;
        double r417516 = r417505 + r417515;
        double r417517 = 3.0;
        double r417518 = r417504 * r417517;
        double r417519 = r417502 / r417518;
        double r417520 = r417516 - r417519;
        double r417521 = r417512 * r417520;
        double r417522 = r417509 - r417521;
        double r417523 = r417502 * r417522;
        double r417524 = exp(r417523);
        double r417525 = r417501 * r417524;
        double r417526 = r417500 + r417525;
        double r417527 = r417500 / r417526;
        return r417527;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r417528 = x;
        double r417529 = y;
        double r417530 = 2.0;
        double r417531 = z;
        double r417532 = t;
        double r417533 = a;
        double r417534 = r417532 + r417533;
        double r417535 = sqrt(r417534);
        double r417536 = r417531 * r417535;
        double r417537 = r417536 / r417532;
        double r417538 = b;
        double r417539 = c;
        double r417540 = r417538 - r417539;
        double r417541 = 5.0;
        double r417542 = 6.0;
        double r417543 = r417541 / r417542;
        double r417544 = r417533 + r417543;
        double r417545 = 3.0;
        double r417546 = r417532 * r417545;
        double r417547 = r417530 / r417546;
        double r417548 = r417544 - r417547;
        double r417549 = r417540 * r417548;
        double r417550 = r417537 - r417549;
        double r417551 = exp(r417550);
        double r417552 = log(r417551);
        double r417553 = r417530 * r417552;
        double r417554 = exp(r417553);
        double r417555 = r417529 * r417554;
        double r417556 = r417528 + r417555;
        double r417557 = r417528 / r417556;
        return r417557;
}

Target

Original	3.8
Target	3.1
Herbie	3.8

\[\begin{array}{l} \mathbf{if}\;t \lt -2.118326644891581057561884576920117070548 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333333703407674875052180141211 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.196588770651547088010424937268931048836 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Derivation

Initial program 3.8
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-log-exp8.0
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}\right)}}\]
Applied add-log-exp16.3
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\log \left(e^{\frac{z \cdot \sqrt{t + a}}{t}}\right)} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)\right)}}\]
Applied diff-log16.3
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}}\right)}}}\]
Simplified3.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}}\]
Final simplification3.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2 (/ (- (* (* z (sqrt (+ t a))) (* (* 3 t) (- a (/ 5 6)))) (* (- (* (+ (/ 5 6) a) (* 3 t)) 2) (* (- a (/ 5 6)) (* (- b c) t)))) (* (* (* t t) 3) (- a (/ 5 6))))))))) (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3))))))))))))

  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))

Error

Try it out

Target

Derivation

Reproduce

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