Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B

Average Error: 6.0 → 0.2

Time: 12.4s

Precision: binary64

Cost: 1088

Math

\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

↓

\[x \cdot x - \left(y \cdot \left(t \cdot -4\right) - z \cdot \left(z \cdot \left(y \cdot -4\right)\right)\right) \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x x) (* (* y 4.0) (- (* z z) t))))

↓

(FPCore (x y z t)
 :precision binary64
 (- (* x x) (- (* y (* t -4.0)) (* z (* z (* y -4.0))))))

C

double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

↓

double code(double x, double y, double z, double t) {
	return (x * x) - ((y * (t * -4.0)) - (z * (z * (y * -4.0))));
}

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 * x) - ((y * 4.0d0) * ((z * z) - 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 = (x * x) - ((y * (t * (-4.0d0))) - (z * (z * (y * (-4.0d0)))))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

↓

public static double code(double x, double y, double z, double t) {
	return (x * x) - ((y * (t * -4.0)) - (z * (z * (y * -4.0))));
}

Python

def code(x, y, z, t):
	return (x * x) - ((y * 4.0) * ((z * z) - t))

↓

def code(x, y, z, t):
	return (x * x) - ((y * (t * -4.0)) - (z * (z * (y * -4.0))))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(Float64(y * 4.0) * Float64(Float64(z * z) - t)))
end

↓

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(Float64(y * Float64(t * -4.0)) - Float64(z * Float64(z * Float64(y * -4.0)))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * x) - ((y * 4.0) * ((z * z) - t));
end

↓

function tmp = code(x, y, z, t)
	tmp = (x * x) - ((y * (t * -4.0)) - (z * (z * (y * -4.0))));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(N[(y * 4.0), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] - N[(z * N[(z * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	6.0
Target	6.0
Herbie	0.2

\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right) \]

Derivation

1. Initial program 6.0

   \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

2. Applied egg-rr 6.0

   \[\leadsto x \cdot x - \color{blue}{\left(\left(z \cdot z\right) \cdot \left(y \cdot 4\right) + \left(-t\right) \cdot \left(y \cdot 4\right)\right)} \]

3. Applied egg-rr 0.2

   \[\leadsto x \cdot x - \color{blue}{\left(z \cdot \left(z \cdot \left(y \cdot 4\right)\right) - y \cdot \left(4 \cdot t\right)\right)} \]

4. Final simplification 0.2

   \[\leadsto x \cdot x - \left(y \cdot \left(t \cdot -4\right) - z \cdot \left(z \cdot \left(y \cdot -4\right)\right)\right) \]

Alternatives

Alternative 1
Error	17.2
Cost	1876

\[\begin{array}{l} t_1 := \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{if}\;x \cdot x \leq 3.189122409663858 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 2.9970093118197932 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \left(z \cdot \left(y \cdot -4\right)\right)\\ \mathbf{elif}\;x \cdot x \leq 55845.96095437452:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 6.769647036668995 \cdot 10^{+20}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \cdot x \leq 9.96294319264696 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	28.5
Cost	1620

\[\begin{array}{l} t_1 := \left(y \cdot 4\right) \cdot t\\ \mathbf{if}\;x \cdot x \leq 1.3379440900550147 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 3.013087825218295 \cdot 10^{-194}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \cdot x \leq 6.096319104618086 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 5.732789429636953 \cdot 10^{-84}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;x \cdot x \leq 5.282287698555033 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 3
Error	28.5
Cost	1504

\[\begin{array}{l} t_1 := z \cdot \left(z \cdot \left(y \cdot -4\right)\right)\\ t_2 := \left(y \cdot 4\right) \cdot t\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.006483327713974754:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq -3.327773238495874 \cdot 10^{-29}:\\ \;\;\;\;\left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \leq -2.0198680068272004 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.244710198496247 \cdot 10^{-303}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 1.2409105294748365 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.57958659221689 \cdot 10^{-11}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 8374023460207177000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	9.6
Cost	1236

\[\begin{array}{l} t_1 := x \cdot x - y \cdot \left(t \cdot -4\right)\\ t_2 := z \cdot \left(z \cdot \left(y \cdot -4\right)\right)\\ t_3 := \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.006483327713974754:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4645794879292476 \cdot 10^{-25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.465915319743674 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{+140}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	7.5
Cost	1232

\[\begin{array}{l} t_1 := x \cdot x + \left(z \cdot z\right) \cdot \left(y \cdot -4\right)\\ t_2 := z \cdot \left(z \cdot \left(y \cdot -4\right)\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4645794879292476 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8374023460207177000:\\ \;\;\;\;x \cdot x - y \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;z \leq 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	1.0
Cost	1092

\[\begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+297}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \left(y \cdot -4\right)\right)\\ \end{array} \]

Alternative 7
Error	27.9
Cost	848

\[\begin{array}{l} t_1 := \left(y \cdot 4\right) \cdot t\\ \mathbf{if}\;x \leq -1.2755911348172126 \cdot 10^{-72}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 5.431222343306359 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7358248256141215 \cdot 10^{-97}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 3.022006735122268 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 8
Error	41.3
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2022295 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))