Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Average Error: 11.8 → 2.2

Time: 5.1s

Precision: binary64

Math

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

↓

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

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

↓

(FPCore (x y z t) :precision binary64 (* x (- (/ y (- t z)) (/ z (- t z)))))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

↓

double code(double x, double y, double z, double t) {
	return x * ((y / (t - z)) - (z / (t - z)));
}

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 = (x * (y - z)) / (t - z)
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 = x * ((y / (t - z)) - (z / (t - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

↓

public static double code(double x, double y, double z, double t) {
	return x * ((y / (t - z)) - (z / (t - z)));
}

Python

def code(x, y, z, t):
	return (x * (y - z)) / (t - z)

↓

def code(x, y, z, t):
	return x * ((y / (t - z)) - (z / (t - z)))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(y - z)) / Float64(t - z))
end

↓

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / Float64(t - z)) - Float64(z / Float64(t - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (y - z)) / (t - z);
end

↓

function tmp = code(x, y, z, t)
	tmp = x * ((y / (t - z)) - (z / (t - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(x * N[(N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.8
Target	2.2
Herbie	2.2

\[\frac{x}{\frac{t - z}{y - z}} \]

Derivation

1. Initial program 11.8

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

2. Applied *-un-lft-identity_binary64 11.8

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

3. Applied times-frac_binary64 2.2

   \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{t - z}} \]

4. Simplified 2.2

   \[\leadsto \color{blue}{x} \cdot \frac{y - z}{t - z} \]

5. Taylor expanded in y around 0 2.2

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

6. Final simplification 2.2

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

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))