Average Error: 4.0 → 2.8
Time: 40.2s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\left(\frac{5}{6} + \left(a - \frac{\frac{2}{3}}{t}\right)\right) \cdot \left(c - b\right) + \frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot 2}}\]
\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^{\left(\left(\frac{5}{6} + \left(a - \frac{\frac{2}{3}}{t}\right)\right) \cdot \left(c - b\right) + \frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot 2}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r425525 = x;
        double r425526 = y;
        double r425527 = 2.0;
        double r425528 = z;
        double r425529 = t;
        double r425530 = a;
        double r425531 = r425529 + r425530;
        double r425532 = sqrt(r425531);
        double r425533 = r425528 * r425532;
        double r425534 = r425533 / r425529;
        double r425535 = b;
        double r425536 = c;
        double r425537 = r425535 - r425536;
        double r425538 = 5.0;
        double r425539 = 6.0;
        double r425540 = r425538 / r425539;
        double r425541 = r425530 + r425540;
        double r425542 = 3.0;
        double r425543 = r425529 * r425542;
        double r425544 = r425527 / r425543;
        double r425545 = r425541 - r425544;
        double r425546 = r425537 * r425545;
        double r425547 = r425534 - r425546;
        double r425548 = r425527 * r425547;
        double r425549 = exp(r425548);
        double r425550 = r425526 * r425549;
        double r425551 = r425525 + r425550;
        double r425552 = r425525 / r425551;
        return r425552;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r425553 = x;
        double r425554 = y;
        double r425555 = 5.0;
        double r425556 = 6.0;
        double r425557 = r425555 / r425556;
        double r425558 = a;
        double r425559 = 2.0;
        double r425560 = 3.0;
        double r425561 = r425559 / r425560;
        double r425562 = t;
        double r425563 = r425561 / r425562;
        double r425564 = r425558 - r425563;
        double r425565 = r425557 + r425564;
        double r425566 = c;
        double r425567 = b;
        double r425568 = r425566 - r425567;
        double r425569 = r425565 * r425568;
        double r425570 = r425558 + r425562;
        double r425571 = sqrt(r425570);
        double r425572 = cbrt(r425562);
        double r425573 = r425571 / r425572;
        double r425574 = z;
        double r425575 = r425572 * r425572;
        double r425576 = r425574 / r425575;
        double r425577 = r425573 * r425576;
        double r425578 = r425569 + r425577;
        double r425579 = r425578 * r425559;
        double r425580 = exp(r425579);
        double r425581 = r425554 * r425580;
        double r425582 = r425553 + r425581;
        double r425583 = r425553 / r425582;
        return r425583;
}

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

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original4.0
Target3.3
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;t \lt -2.118326644891581057561884576920117070548 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333333703407674875052180141211 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.196588770651547088010424937268931048836 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Derivation

  1. Initial program 4.0

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

  2. Simplified3.4

    \[\leadsto \color{blue}{\frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{a + t}}{t} + \left(c - b\right) \cdot \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right)\right)} + x}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt3.4

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

  5. Applied *-un-lft-identity3.4

    \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{\color{blue}{1 \cdot \left(a + t\right)}}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + \left(c - b\right) \cdot \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

  6. Applied sqrt-prod3.4

    \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\color{blue}{\sqrt{1} \cdot \sqrt{a + t}}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + \left(c - b\right) \cdot \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

  7. Applied times-frac3.4

    \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \color{blue}{\left(\frac{\sqrt{1}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}}\right)} + \left(c - b\right) \cdot \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

  8. Applied associate-*r*2.8

    \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(\color{blue}{\left(z \cdot \frac{\sqrt{1}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}}} + \left(c - b\right) \cdot \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

  9. Simplified2.8

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

  10. Final simplification2.8

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (* 3.0 t) (- a (/ 5.0 6.0)))) (* (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0) (* (- a (/ 5.0 6.0)) (* (- b c) t)))) (* (* (* t t) 3.0) (- a (/ 5.0 6.0))))))))) (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))