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

Average Error: 5.9 → 0.1

Time: 10.4s

Precision: binary64

Cost: 1088

Math

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

↓

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

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 (* 4.0 t)) (* 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 * (4.0 * t)) + (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 * (4.0d0 * t)) + (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 * (4.0 * t)) + (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 * (4.0 * t)) + (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(4.0 * t)) + 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 * (4.0 * t)) + (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[(4.0 * t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(z * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	5.9
Target	5.9
Herbie	0.1

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

Derivation

1. Initial program 5.9

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

2. Applied egg-rr 5.9

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

3. Applied egg-rr 0.1

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

4. Final simplification 0.1

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

Alternatives

Alternative 1
Error	11.0
Cost	3808

\[\begin{array}{l} t_1 := x \cdot x + z \cdot \left(\left(z \cdot y\right) \cdot -4\right)\\ t_2 := z \cdot z - t\\ t_3 := x \cdot x + \left(y \cdot 4\right) \cdot t\\ \mathbf{if}\;t_2 \leq 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+152}:\\ \;\;\;\;4 \cdot \left(y \cdot t - y \cdot \left(z \cdot z\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+268}:\\ \;\;\;\;y \cdot \left(4 \cdot \left(t - z \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.7
Cost	1744

\[\begin{array}{l} t_1 := 4 \cdot \left(y \cdot t - y \cdot \left(z \cdot z\right)\right)\\ t_2 := x \cdot x + \left(y \cdot 4\right) \cdot t\\ \mathbf{if}\;z \cdot z \leq 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 10^{+266}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 3
Error	8.7
Cost	1616

\[\begin{array}{l} t_1 := y \cdot \left(4 \cdot \left(t - z \cdot z\right)\right)\\ t_2 := x \cdot x + \left(y \cdot 4\right) \cdot t\\ \mathbf{if}\;z \cdot z \leq 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 10^{+266}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 4
Error	27.9
Cost	1504

\[\begin{array}{l} t_1 := 4 \cdot \left(y \cdot t\right)\\ t_2 := -4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 5
Error	0.2
Cost	1092

\[\begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+266}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + z \cdot \left(\left(z \cdot y\right) \cdot -4\right)\\ \end{array} \]

Alternative 6
Error	15.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(4 \cdot \left(t - z \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7
Error	26.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-27}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;4 \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 8
Error	41.4
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2022337 
(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))))