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

Average Error: 0.0 → 0.0

Time: 4.1s

Precision: binary64

Cost: 704

Math

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

↓

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

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 z) 2.0)) 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 * z) / 2.0)) + 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 * z) / 2.0d0)) + 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 * z) / 2.0)) + 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 * z) / 2.0)) + 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 * z) / 2.0)) + 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 * z) / 2.0)) + 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 * z), $MachinePrecision] / 2.0), $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. Final simplification 0.0

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

Alternatives

Alternative 1
Error	9.5
Cost	1876

\[\begin{array}{l} t_1 := 0.125 \cdot x + t\\ t_2 := \left(y \cdot z\right) \cdot -0.5\\ t_3 := t + t_2\\ t_4 := 0.125 \cdot x + t_2\\ \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+68}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \cdot z \leq -5:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \cdot z \leq 10:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	29.5
Cost	1248

\[\begin{array}{l} t_1 := y \cdot \left(z \cdot -0.5\right)\\ \mathbf{if}\;x \leq -2.0308738775735248 \cdot 10^{-80}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq -6.88328873309031 \cdot 10^{-205}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -7.070605529581441 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.235099144968928 \cdot 10^{-302}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 4.040736209919038 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4218876128739237 \cdot 10^{-179}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 4.2940514237955987 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.886820263519911 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 3
Error	19.8
Cost	1244

\[\begin{array}{l} t_1 := y \cdot \left(z \cdot -0.5\right)\\ t_2 := 0.125 \cdot x + t\\ \mathbf{if}\;z \leq -1.0324963227037247 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8776026493525175 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+271}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	9.2
Cost	968

\[\begin{array}{l} t_1 := t + \left(y \cdot z\right) \cdot -0.5\\ \mathbf{if}\;y \cdot z \leq -5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq 10:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	27.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.0308738775735248 \cdot 10^{-80}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 9.886820263519911 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 6
Error	39.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022300 
(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))