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

Average Error: 6.0 → 0.1

Time: 8.7s

Precision: binary64

Cost: 1088

Math

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

↓

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

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) (- (* z (* z (* y -4.0))) (* y (* t -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) + ((z * (z * (y * -4.0))) - (y * (t * -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) + ((z * (z * (y * (-4.0d0)))) - (y * (t * (-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) + ((z * (z * (y * -4.0))) - (y * (t * -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) + ((z * (z * (y * -4.0))) - (y * (t * -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(z * Float64(z * Float64(y * -4.0))) - Float64(y * Float64(t * -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) + ((z * (z * (y * -4.0))) - (y * (t * -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[(z * N[(z * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	6.0
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 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 0.1

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

4. Final simplification 0.1

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

Alternatives

Alternative 1
Error	6.8
Cost	1100

\[\begin{array}{l} t_1 := x \cdot x + z \cdot \left(y \cdot \left(z \cdot -4\right)\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-46}:\\ \;\;\;\;\left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{elif}\;z \leq 12.2:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.7
Cost	1096

\[\begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-119}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 10^{+292}:\\ \;\;\;\;\left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 3
Error	0.1
Cost	1092

\[\begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+292}:\\ \;\;\;\;x \cdot x - \left(y \cdot -4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + z \cdot \left(y \cdot \left(z \cdot -4\right)\right)\\ \end{array} \]

Alternative 4
Error	26.0
Cost	976

\[\begin{array}{l} t_1 := \left(y \cdot 4\right) \cdot t\\ t_2 := -4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;z \leq -0.73:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-284}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 7.8:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	14.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+51}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 460000000:\\ \;\;\;\;\left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 6
Error	25.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 45000000:\\ \;\;\;\;\left(y \cdot 4\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7
Error	41.3
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2022325 
(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))))