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

Average Accuracy: 100.0% → 100.0%

Time: 6.1s

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	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Simplified 100.0%

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

   [Start] 100.0	\[ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   sub-neg [=>] 100.0	\[ \color{blue}{\left(\frac{1}{8} \cdot x + \left(-\frac{y \cdot z}{2}\right)\right)} + t \]
   +-commutative [=>] 100.0	\[ \color{blue}{\left(\left(-\frac{y \cdot z}{2}\right) + \frac{1}{8} \cdot x\right)} + t \]
   neg-sub0 [=>] 100.0	\[ \left(\color{blue}{\left(0 - \frac{y \cdot z}{2}\right)} + \frac{1}{8} \cdot x\right) + t \]
   associate-+l- [=>] 100.0	\[ \color{blue}{\left(0 - \left(\frac{y \cdot z}{2} - \frac{1}{8} \cdot x\right)\right)} + t \]
   sub-neg [=>] 100.0	\[ \left(0 - \color{blue}{\left(\frac{y \cdot z}{2} + \left(-\frac{1}{8} \cdot x\right)\right)}\right) + t \]
   +-commutative [=>] 100.0	\[ \left(0 - \color{blue}{\left(\left(-\frac{1}{8} \cdot x\right) + \frac{y \cdot z}{2}\right)}\right) + t \]
   associate--r+ [=>] 100.0	\[ \color{blue}{\left(\left(0 - \left(-\frac{1}{8} \cdot x\right)\right) - \frac{y \cdot z}{2}\right)} + t \]
   neg-sub0 [<=] 100.0	\[ \left(\color{blue}{\left(-\left(-\frac{1}{8} \cdot x\right)\right)} - \frac{y \cdot z}{2}\right) + t \]
   distribute-rgt-neg-in [=>] 100.0	\[ \left(\left(-\color{blue}{\frac{1}{8} \cdot \left(-x\right)}\right) - \frac{y \cdot z}{2}\right) + t \]
   distribute-rgt-neg-in [=>] 100.0	\[ \left(\color{blue}{\frac{1}{8} \cdot \left(-\left(-x\right)\right)} - \frac{y \cdot z}{2}\right) + t \]
   metadata-eval [=>] 100.0	\[ \left(\color{blue}{0.125} \cdot \left(-\left(-x\right)\right) - \frac{y \cdot z}{2}\right) + t \]
   remove-double-neg [=>] 100.0	\[ \left(0.125 \cdot \color{blue}{x} - \frac{y \cdot z}{2}\right) + t \]
   associate-*l/ [<=] 100.0	\[ \left(0.125 \cdot x - \color{blue}{\frac{y}{2} \cdot z}\right) + t \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	53.0%
Cost	1248

\[\begin{array}{l} t_1 := z \cdot \left(y \cdot -0.5\right)\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-93}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-307}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-174}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+58}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 2
Accuracy	86.2%
Cost	972

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot z\right)\\ t_2 := 0.125 \cdot x + t\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;t - t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+57}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	65.2%
Cost	850

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-111} \lor \neg \left(z \leq 4.4 \cdot 10^{+138} \lor \neg \left(z \leq 3.3 \cdot 10^{+187}\right) \land z \leq 5.6 \cdot 10^{+255}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 4
Accuracy	56.3%
Cost	721

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+21}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;\neg \left(x \leq 7.5 \cdot 10^{+49}\right) \land x \leq 1.18 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 5
Accuracy	86.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-26} \lor \neg \left(x \leq 1.9 \cdot 10^{+58}\right):\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6
Accuracy	36.8%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023151 
(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))