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

Average Error: 0.0 → 0.0

Time: 5.5s

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	8.4
Cost	1616

\[\begin{array}{l} t_1 := \left(y \cdot z\right) \cdot -0.5\\ t_2 := 0.125 \cdot x + t_1\\ t_3 := t + t_1\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \cdot z \leq 1000000:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{elif}\;y \cdot z \leq 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	29.3
Cost	1244

\[\begin{array}{l} t_1 := z \cdot \left(y \cdot -0.5\right)\\ \mathbf{if}\;x \leq -50726982.145543836:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq -1.3725320958864267 \cdot 10^{-63}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -5.21123273732716 \cdot 10^{-97}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 3.008106036162064 \cdot 10^{-218}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.704565322033163 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.565213309629648 \cdot 10^{-73}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.4665227109244428 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 3
Error	20.3
Cost	848

\[\begin{array}{l} t_1 := 0.125 \cdot x + t\\ t_2 := z \cdot \left(y \cdot -0.5\right)\\ \mathbf{if}\;x \leq 3.008106036162064 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.704565322033163 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.565213309629648 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.013584401317891 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	27.8
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -50726982.145543836:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq -1.3725320958864267 \cdot 10^{-63}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -5.21123273732716 \cdot 10^{-97}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 2.8750844697565803 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 5
Error	9.4
Cost	712

\[\begin{array}{l} t_1 := 0.125 \cdot x + t\\ \mathbf{if}\;x \leq -3.440215225959135 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.616504301859124 \cdot 10^{+74}:\\ \;\;\;\;t + \left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	39.6
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022294 
(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))