Average Error: 7.3 → 1.0
Time: 15.9s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{t - z}
(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (*
  (/ (* (cbrt x) (cbrt x)) (* (cbrt (- y z)) (cbrt (- y z))))
  (/ (/ (cbrt x) (cbrt (- y z))) (- 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(x) * cbrt(x)) / (cbrt(y - z) * cbrt(y - z))) * ((cbrt(x) / cbrt(y - z)) / (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

Original7.3
Target7.9
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.3

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

  2. Simplified1.9

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

  4. Applied *-un-lft-identity_binary64_150821.9

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

  5. Applied add-cube-cbrt_binary64_151172.5

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

  6. Applied add-cube-cbrt_binary64_151172.6

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

  7. Applied times-frac_binary64_150882.6

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

  8. Applied times-frac_binary64_150881.0

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2021176 
(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))))