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

Average Error: 0.1 → 0.1

Time: 3.7s

Precision: binary64

Cost: 704

Math

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

↓

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

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) -0.5)) 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) * -0.5)) + 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) * (-0.5d0))) + 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) * -0.5)) + 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) * -0.5)) + 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) * -0.5)) + 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) * -0.5)) + 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] * -0.5), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Target

Original	0.1
Target	0.0
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot -0.5 + 0.125 \cdot x\right)} + t \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	12.3
Cost	840

\[\begin{array}{l} t_1 := \left(y \cdot z\right) \cdot -0.5\\ \mathbf{if}\;y \cdot z \leq -1.758284875846781 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq 7.1875901071827 \cdot 10^{+110}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.9
Cost	712

\[\begin{array}{l} t_1 := 0.125 \cdot x + t\\ \mathbf{if}\;x \leq -6.400776139917759 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 245513750201185.4:\\ \;\;\;\;t + y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	32.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -1.1442214317039235 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.0991879081952344 \cdot 10^{-78}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Error	40.2
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022316 
(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))