Average Error: 5.9 → 0.1
Time: 6.6s
Precision: binary64
Cost: 704
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{x + -1}{y \cdot \frac{-3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{x + -1}{y \cdot \frac{-3}{3 - x}}
(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))
↓
(FPCore (x y) :precision binary64 (/ (+ x -1.0) (* y (/ -3.0 (- 3.0 x)))))
double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}
↓
double code(double x, double y) {
	return (x + -1.0) / (y * (-3.0 / (3.0 - x)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.9
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Alternatives

Alternative 1
Error1.3
Cost21440
\[\sqrt[3]{\frac{1 - x}{\frac{y}{\frac{3 - x}{3}}}} \cdot \left(\sqrt[3]{\frac{1 - x}{\frac{y}{\frac{3 - x}{3}}}} \cdot \sqrt[3]{\frac{1 - x}{\frac{y}{\frac{3 - x}{3}}}}\right)\]
Alternative 2
Error6.9
Cost21440
\[\sqrt[3]{\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}} \cdot \left(\sqrt[3]{\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}} \cdot \sqrt[3]{\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}}\right)\]
Alternative 3
Error6.1
Cost20416
\[\frac{\left(\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}\right) \cdot \left(\sqrt[3]{1 - x} \cdot \left(3 - x\right)\right)}{y \cdot 3}\]
Alternative 4
Error2.0
Cost20416
\[\frac{\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}}{y} \cdot \left(\sqrt[3]{1 - x} \cdot \frac{3 - x}{3}\right)\]
Alternative 5
Error35.3
Cost14272
\[\sqrt{\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}} \cdot \sqrt{\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}}\]
Alternative 6
Error31.6
Cost13760
\[\left(1 + \sqrt{x}\right) \cdot \frac{1 - \sqrt{x}}{\frac{y}{\frac{3 - x}{3}}}\]
Alternative 7
Error43.2
Cost13568
\[\sqrt[3]{{\left(\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\right)}^{3}}\]
Alternative 8
Error37.2
Cost13568
\[\frac{1 - x}{\sqrt[3]{{\left(\frac{y}{\frac{3 - x}{3}}\right)}^{3}}}\]
Alternative 9
Error15.2
Cost8064
\[\frac{\left(9 - x \cdot x\right) \cdot \left(1 - {x}^{3}\right)}{\left(y \cdot 3\right) \cdot \left(\left(x + 3\right) \cdot \left(1 + \left(x + x \cdot x\right)\right)\right)}\]
Alternative 10
Error13.4
Cost1472
\[\frac{\left(1 - x \cdot x\right) \cdot \left(9 - x \cdot x\right)}{\left(y \cdot 3\right) \cdot \left(\left(x + 1\right) \cdot \left(x + 3\right)\right)}\]
Alternative 11
Error11.0
Cost1088
\[\frac{\left(3 - x\right) \cdot \left(1 - x \cdot x\right)}{\left(y \cdot 3\right) \cdot \left(x + 1\right)}\]
Alternative 12
Error5.7
Cost832
\[\frac{1}{y} - \frac{x \cdot \left(1.3333333333333333 - x \cdot 0.3333333333333333\right)}{y}\]
Alternative 13
Error5.8
Cost832
\[\frac{1}{\frac{y \cdot 3}{\left(1 - x\right) \cdot \left(3 - x\right)}}\]
Alternative 14
Error0.2
Cost832
\[\frac{1 - x}{y \cdot \left(3 \cdot \frac{1}{3 - x}\right)}\]
Alternative 15
Error0.2
Cost704
\[\frac{\left(3 - x\right) \cdot \frac{1 - x}{y}}{3}\]
Alternative 16
Error0.1
Cost704
\[\frac{1 - x}{\frac{y}{\frac{3 - x}{3}}}\]
Alternative 17
Error6.0
Cost704
\[\left(\left(1 - x\right) \cdot \left(3 - x\right)\right) \cdot \frac{0.3333333333333333}{y}\]
Alternative 18
Error0.1
Cost704
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]
Alternative 19
Error5.9
Cost704
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
Alternative 20
Error47.0
Cost576
\[\frac{x \cdot \left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)}{y}\]
Alternative 21
Error20.9
Cost576
\[\frac{1}{y} - 1.3333333333333333 \cdot \frac{x}{y}\]
Alternative 22
Error41.8
Cost576
\[\frac{1 - x}{y \cdot \frac{-3}{x}}\]
Alternative 23
Error41.9
Cost576
\[\frac{1 - x}{-3 \cdot \frac{y}{x}}\]
Alternative 24
Error47.0
Cost576
\[\frac{x \cdot \left(x + -4\right)}{y \cdot 3}\]
Alternative 25
Error21.1
Cost576
\[\frac{3 - x \cdot 4}{y \cdot 3}\]
Alternative 26
Error41.7
Cost448
\[0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\]
Alternative 27
Error41.7
Cost448
\[\frac{x \cdot \frac{x}{y}}{3}\]
Alternative 28
Error47.3
Cost448
\[\frac{x \cdot x}{y \cdot 3}\]
Alternative 29
Error47.3
Cost448
\[0.3333333333333333 \cdot \frac{x \cdot x}{y}\]
Alternative 30
Error21.3
Cost320
\[\frac{1 - x}{y}\]
Alternative 31
Error21.2
Cost192
\[\frac{1}{y}\]
Alternative 32
Error61.8
Cost64
\[1\]
Alternative 33
Error61.8
Cost64
\[0\]
Alternative 34
Error61.8
Cost64
\[-1\]

Error

Derivation

  1. Initial program 5.9

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied associate-/l*_binary64_160000.3

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

  4. Simplified0.1

    \[\leadsto \frac{1 - x}{\color{blue}{\frac{y}{\frac{3 - x}{3}}}}\]
  5. Using strategy rm

  6. Applied div-inv_binary64_160520.2

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

  7. Simplified0.2

    \[\leadsto \frac{1 - x}{y \cdot \color{blue}{\left(\frac{1}{3 - x} \cdot 3\right)}}\]
  8. Using strategy rm

  9. Applied frac-2neg_binary64_160660.2

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

  10. Simplified0.2

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

  11. Simplified0.1

    \[\leadsto \frac{x + -1}{\color{blue}{y \cdot \frac{-3}{3 - x}}}\]

  12. Simplified0.1

    \[\leadsto \color{blue}{\frac{x + -1}{y \cdot \frac{-3}{3 - x}}}\]

  13. Final simplification0.1

    \[\leadsto \frac{x + -1}{y \cdot \frac{-3}{3 - x}}\]

Reproduce

herbie shell --seed 2021042 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))