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

Average Error: 0.0 → 0.0

Time: 8.1s

Precision: binary64

Cost: 832

Math

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

↓

\[\left(\frac{1}{8} \cdot x - \left(z \cdot 0.5\right) \cdot y\right) + t \]

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
 (+ (- (* (/ 1.0 8.0) x) (* (* z 0.5) y)) 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 (((1.0 / 8.0) * x) - ((z * 0.5) * y)) + 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 = (((1.0d0 / 8.0d0) * x) - ((z * 0.5d0) * y)) + 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 (((1.0 / 8.0) * x) - ((z * 0.5) * y)) + 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 (((1.0 / 8.0) * x) - ((z * 0.5) * y)) + 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(Float64(1.0 / 8.0) * x) - Float64(Float64(z * 0.5) * y)) + 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 = (((1.0 / 8.0) * x) - ((z * 0.5) * y)) + 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[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(z * 0.5), $MachinePrecision] * y), $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. Applied egg-rr 0.0

   \[\leadsto \left(\frac{1}{8} \cdot x - \color{blue}{\left(z \cdot 0.5\right) \cdot y}\right) + t \]

Alternatives

Alternative 1
Error	8.7
Cost	1104

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot z\right)\\ t_2 := 0.125 \cdot x + t\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 29000:\\ \;\;\;\;t - t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+171}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	28.5
Cost	984

\[\begin{array}{l} t_1 := -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-303}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-138}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3
Error	29.6
Cost	984

\[\begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-183}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-233}:\\ \;\;\;\;\left(-0.5 \cdot z\right) \cdot y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-137}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-45}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+73}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Error	12.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+61}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+135}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;\left(-0.5 \cdot z\right) \cdot y\\ \end{array} \]

Alternative 5
Error	8.5
Cost	712

\[\begin{array}{l} t_1 := 0.125 \cdot x + t\\ \mathbf{if}\;x \leq -1.62 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.0075:\\ \;\;\;\;t - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	0.0
Cost	704

\[\left(0.125 \cdot x + t\right) - 0.5 \cdot \left(y \cdot z\right) \]

Alternative 7
Error	0.0
Cost	704

\[\left(\left(y \cdot z\right) \cdot -0.5 + t\right) - -0.125 \cdot x \]

Alternative 8
Error	27.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+74}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	39.9
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023010 
(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))