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

Average Error: 0.0 → 0.0

Time: 4.6s

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. Simplified 0.0

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

   [Start] 0.0	\[ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   metadata-eval [=>] 0.0	\[ \left(\color{blue}{0.125} \cdot x - \frac{y \cdot z}{2}\right) + t \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	14.6
Cost	1500

\[\begin{array}{l} t_1 := 0.125 \cdot x + t\\ t_2 := y \cdot \left(z \cdot 0.5\right)\\ t_3 := t - t_2\\ \mathbf{if}\;z \leq -4 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+181}:\\ \;\;\;\;0.125 \cdot x - t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	15.1
Cost	1240

\[\begin{array}{l} t_1 := 0.125 \cdot x + t\\ t_2 := t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	30.2
Cost	1116

\[\begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -370000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-181}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 45:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+150}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Error	29.8
Cost	984

\[\begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -30000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1950000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+150}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5
Error	12.0
Cost	840

\[\begin{array}{l} t_1 := -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -5.5 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \cdot z \leq 7.2 \cdot 10^{+143}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	40.1
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023090 
(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))