Average Error: 8.1 → 1.2
Time: 13.6s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}}
(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (*
  (/
   (* (cbrt 1.0) (cbrt 1.0))
   (/
    (* (cbrt (- y z)) (cbrt (- y z)))
    (/ (* (cbrt x) (cbrt x)) (* (cbrt (- t z)) (cbrt (- t z))))))
  (/ (cbrt 1.0) (/ (cbrt (- y z)) (/ (cbrt x) (cbrt (- t z)))))))
double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}
↓
double code(double x, double y, double z, double t) {
	return ((cbrt(1.0) * cbrt(1.0)) / ((cbrt(y - z) * cbrt(y - z)) / ((cbrt(x) * cbrt(x)) / (cbrt(t - z) * cbrt(t - z))))) * (cbrt(1.0) / (cbrt(y - z) / (cbrt(x) / cbrt(t - z))));
}

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

Original8.1
Target8.9
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 8.1

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

  3. Applied clear-num_binary64_208788.4

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

  4. Simplified2.4

    \[\leadsto \frac{1}{\color{blue}{\frac{y - z}{\frac{x}{t - z}}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt_binary64_209143.0

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

  7. Applied add-cube-cbrt_binary64_209143.2

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

  8. Applied times-frac_binary64_208853.2

    \[\leadsto \frac{1}{\frac{y - z}{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}}}\]

  9. Applied add-cube-cbrt_binary64_209143.3

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

  10. Applied times-frac_binary64_208851.7

    \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}} \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}}}\]

  11. Applied add-cube-cbrt_binary64_209141.7

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

  12. Applied times-frac_binary64_208851.2

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}}}\]

  13. Final simplification1.2

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{t - z}}}}\]

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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