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

↓

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

\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 \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{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 r495631 = x;
        double r495632 = y;
        double r495633 = 2.0;
        double r495634 = z;
        double r495635 = t;
        double r495636 = a;
        double r495637 = r495635 + r495636;
        double r495638 = sqrt(r495637);
        double r495639 = r495634 * r495638;
        double r495640 = r495639 / r495635;
        double r495641 = b;
        double r495642 = c;
        double r495643 = r495641 - r495642;
        double r495644 = 5.0;
        double r495645 = 6.0;
        double r495646 = r495644 / r495645;
        double r495647 = r495636 + r495646;
        double r495648 = 3.0;
        double r495649 = r495635 * r495648;
        double r495650 = r495633 / r495649;
        double r495651 = r495647 - r495650;
        double r495652 = r495643 * r495651;
        double r495653 = r495640 - r495652;
        double r495654 = r495633 * r495653;
        double r495655 = exp(r495654);
        double r495656 = r495632 * r495655;
        double r495657 = r495631 + r495656;
        double r495658 = r495631 / r495657;
        return r495658;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r495659 = x;
        double r495660 = y;
        double r495661 = 2.0;
        double r495662 = z;
        double r495663 = t;
        double r495664 = cbrt(r495663);
        double r495665 = r495664 * r495664;
        double r495666 = r495662 / r495665;
        double r495667 = a;
        double r495668 = r495663 + r495667;
        double r495669 = sqrt(r495668);
        double r495670 = r495669 / r495664;
        double r495671 = r495666 * r495670;
        double r495672 = b;
        double r495673 = c;
        double r495674 = r495672 - r495673;
        double r495675 = 5.0;
        double r495676 = 6.0;
        double r495677 = r495675 / r495676;
        double r495678 = r495667 + r495677;
        double r495679 = 3.0;
        double r495680 = r495663 * r495679;
        double r495681 = r495661 / r495680;
        double r495682 = r495678 - r495681;
        double r495683 = r495674 * r495682;
        double r495684 = r495671 - r495683;
        double r495685 = r495661 * r495684;
        double r495686 = exp(r495685);
        double r495687 = r495660 * r495686;
        double r495688 = r495659 + r495687;
        double r495689 = r495659 / r495688;
        return r495689;
}

Target

Original	4.0
Target	3.1
Herbie	2.8

\[\begin{array}{l} \mathbf{if}\;t \lt -2.1183266448915811 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.83333333333333337 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.19658877065154709 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Derivation

Initial program 4.0
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt4.0
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Applied times-frac2.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Final simplification2.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

Reproduce

herbie shell --seed 2020089 
(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

In
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