Average Error: 4.7 → 5.3
Time: 7.0s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[x \cdot \left({\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)}^{3} - \frac{t}{1 - z}\right)\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
x \cdot \left({\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)}^{3} - \frac{t}{1 - z}\right)
double f(double x, double y, double z, double t) {
        double r271472 = x;
        double r271473 = y;
        double r271474 = z;
        double r271475 = r271473 / r271474;
        double r271476 = t;
        double r271477 = 1.0;
        double r271478 = r271477 - r271474;
        double r271479 = r271476 / r271478;
        double r271480 = r271475 - r271479;
        double r271481 = r271472 * r271480;
        return r271481;
}
↓
double f(double x, double y, double z, double t) {
        double r271482 = x;
        double r271483 = y;
        double r271484 = cbrt(r271483);
        double r271485 = z;
        double r271486 = cbrt(r271485);
        double r271487 = r271484 / r271486;
        double r271488 = 3.0;
        double r271489 = pow(r271487, r271488);
        double r271490 = t;
        double r271491 = 1.0;
        double r271492 = r271491 - r271485;
        double r271493 = r271490 / r271492;
        double r271494 = r271489 - r271493;
        double r271495 = r271482 * r271494;
        return r271495;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original4.7
Target4.1
Herbie5.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.623226303312042442144691872793570510727 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.413394492770230216018398633584271456447 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Initial program 4.7

    \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
  2. Using strategy rm

  3. Applied div-inv4.7

    \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{t \cdot \frac{1}{1 - z}}\right)\]
  4. Using strategy rm

  5. Applied sub-neg4.7

    \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} + \left(-t \cdot \frac{1}{1 - z}\right)\right)}\]

  6. Applied distribute-lft-in4.7

    \[\leadsto \color{blue}{x \cdot \frac{y}{z} + x \cdot \left(-t \cdot \frac{1}{1 - z}\right)}\]

  7. Simplified4.7

    \[\leadsto x \cdot \frac{y}{z} + \color{blue}{\left(-x\right) \cdot \frac{t}{1 - z}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt5.2

    \[\leadsto x \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}} + \left(-x\right) \cdot \frac{t}{1 - z}\]

  10. Applied add-cube-cbrt5.3

    \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}} + \left(-x\right) \cdot \frac{t}{1 - z}\]

  11. Applied times-frac5.3

    \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)} + \left(-x\right) \cdot \frac{t}{1 - z}\]

  12. Applied associate-*r*1.9

    \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}} + \left(-x\right) \cdot \frac{t}{1 - z}\]

  13. Final simplification5.3

    \[\leadsto x \cdot \left({\left(\frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)}^{3} - \frac{t}{1 - z}\right)\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1 z)))) -7.62322630331204244e-196) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 1.41339449277023022e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z)))))))

  (* x (- (/ y z) (/ t (- 1 z)))))