Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Average Error: 0.0 → 0.0

Time: 5.7s

Precision: binary64

Cost: 704

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

↓

\[\left(0.125 \cdot x - \frac{y}{2} \cdot z\right) + t \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

↓

(FPCore (x y z t) :precision binary64 (+ (- (* 0.125 x) (* (/ y 2.0) z)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

↓

double code(double x, double y, double z, double t) {
	return ((0.125 * x) - ((y / 2.0) * z)) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((0.125d0 * x) - ((y / 2.0d0) * z)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

↓

public static double code(double x, double y, double z, double t) {
	return ((0.125 * x) - ((y / 2.0) * z)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

↓

def code(x, y, z, t):
	return ((0.125 * x) - ((y / 2.0) * z)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

↓

function code(x, y, z, t)
	return Float64(Float64(Float64(0.125 * x) - Float64(Float64(y / 2.0) * z)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

↓

function tmp = code(x, y, z, t)
	tmp = ((0.125 * x) - ((y / 2.0) * z)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(N[(N[(0.125 * x), $MachinePrecision] - N[(N[(y / 2.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y \]

Derivation

1. Initial program 0.0

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y}{2} \cdot z\right) + t} \]
   Proof

   [Start] 0.0	\[ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   associate-+l- [=>] 0.0	\[ \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]
   sub-neg [=>] 0.0	\[ \color{blue}{\frac{1}{8} \cdot x + \left(-\left(\frac{y \cdot z}{2} - t\right)\right)} \]
   neg-mul-1 [=>] 0.0	\[ \frac{1}{8} \cdot x + \color{blue}{-1 \cdot \left(\frac{y \cdot z}{2} - t\right)} \]
   *-commutative [=>] 0.0	\[ \frac{1}{8} \cdot x + \color{blue}{\left(\frac{y \cdot z}{2} - t\right) \cdot -1} \]
   cancel-sign-sub [<=] 0.0	\[ \color{blue}{\frac{1}{8} \cdot x - \left(-\left(\frac{y \cdot z}{2} - t\right)\right) \cdot -1} \]
   *-commutative [=>] 0.0	\[ \frac{1}{8} \cdot x - \color{blue}{-1 \cdot \left(-\left(\frac{y \cdot z}{2} - t\right)\right)} \]
   cancel-sign-sub-inv [=>] 0.0	\[ \color{blue}{\frac{1}{8} \cdot x + \left(--1\right) \cdot \left(-\left(\frac{y \cdot z}{2} - t\right)\right)} \]
   metadata-eval [=>] 0.0	\[ \frac{1}{8} \cdot x + \color{blue}{1} \cdot \left(-\left(\frac{y \cdot z}{2} - t\right)\right) \]
   neg-sub0 [=>] 0.0	\[ \frac{1}{8} \cdot x + 1 \cdot \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - t\right)\right)} \]
   associate-+l- [<=] 0.0	\[ \frac{1}{8} \cdot x + 1 \cdot \color{blue}{\left(\left(0 - \frac{y \cdot z}{2}\right) + t\right)} \]
   neg-sub0 [<=] 0.0	\[ \frac{1}{8} \cdot x + 1 \cdot \left(\color{blue}{\left(-\frac{y \cdot z}{2}\right)} + t\right) \]
   distribute-lft-in [=>] 0.0	\[ \frac{1}{8} \cdot x + \color{blue}{\left(1 \cdot \left(-\frac{y \cdot z}{2}\right) + 1 \cdot t\right)} \]
   *-lft-identity [=>] 0.0	\[ \frac{1}{8} \cdot x + \left(1 \cdot \left(-\frac{y \cdot z}{2}\right) + \color{blue}{t}\right) \]
   associate-+r+ [=>] 0.0	\[ \color{blue}{\left(\frac{1}{8} \cdot x + 1 \cdot \left(-\frac{y \cdot z}{2}\right)\right) + t} \]

3. Final simplification 0.0

   \[\leadsto \left(0.125 \cdot x - \frac{y}{2} \cdot z\right) + t \]

Alternatives

Alternative 1
Error	30.9
Cost	2140

\[\begin{array}{l} t_1 := \left(y \cdot z\right) \cdot -0.5\\ \mathbf{if}\;y \cdot z \leq -9.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq -5.5 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq -4.3 \cdot 10^{-231}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;y \cdot z \leq 3.1 \cdot 10^{-230}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \cdot z \leq 10^{+43}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.5
Cost	1097

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -6.5 \cdot 10^{+52} \lor \neg \left(y \cdot z \leq 1.12 \cdot 10^{+15}\right):\\ \;\;\;\;0.125 \cdot x + \left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 3
Error	8.4
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -5.9 \cdot 10^{+82} \lor \neg \left(y \cdot z \leq 8.2 \cdot 10^{+43}\right):\\ \;\;\;\;t + \left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 4
Error	12.1
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -2.75 \cdot 10^{+91} \lor \neg \left(y \cdot z \leq 1.4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 5
Error	28.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-13}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6
Error	40.0
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023073 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))