Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B

Average Error: 25.1 → 0.5

Time: 18.2s

Precision: binary64

Cost: 13572

Math

\[x \cdot \sqrt{y \cdot y - z \cdot z} \]

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -5.492534920634091 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \left(\sqrt{\left(-z\right) - y} \cdot \sqrt{z - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (sqrt (- (* y y) (* z z)))))

↓

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.492534920634091e-284)
   (* x (* (sqrt (- (- z) y)) (sqrt (- z y))))
   (* y x)))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.492534920634091e-284) {
		tmp = x * (sqrt((-z - y)) * sqrt((z - y)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * sqrt(((y * y) - (z * z)))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.492534920634091d-284)) then
        tmp = x * (sqrt((-z - y)) * sqrt((z - y)))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return x * Math.sqrt(((y * y) - (z * z)));
}

↓

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.492534920634091e-284) {
		tmp = x * (Math.sqrt((-z - y)) * Math.sqrt((z - y)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	return x * math.sqrt(((y * y) - (z * z)))

↓

def code(x, y, z):
	tmp = 0
	if y <= -5.492534920634091e-284:
		tmp = x * (math.sqrt((-z - y)) * math.sqrt((z - y)))
	else:
		tmp = y * x
	return tmp

Julia

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

↓

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.492534920634091e-284)
		tmp = Float64(x * Float64(sqrt(Float64(Float64(-z) - y)) * sqrt(Float64(z - y))));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.492534920634091e-284)
		tmp = x * (sqrt((-z - y)) * sqrt((z - y)));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := If[LessEqual[y, -5.492534920634091e-284], N[(x * N[(N[Sqrt[N[((-z) - y), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(z - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]

Target

Original	25.1
Target	0.6
Herbie	0.5

\[\begin{array}{l} \mathbf{if}\;y < 2.5816096488251695 \cdot 10^{-278}:\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\sqrt{y + z} \cdot \sqrt{y - z}\right)\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if y < -5.4925349206340911e-284

   1. Initial program 25.2

      \[x \cdot \sqrt{y \cdot y - z \cdot z} \]

   2. Applied egg-rr 0.4

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

   if -5.4925349206340911e-284 < y

   1. Initial program 24.9

      \[x \cdot \sqrt{y \cdot y - z \cdot z} \]

   2. Taylor expanded in y around inf 0.6

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.492534920634091 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \left(\sqrt{\left(-z\right) - y} \cdot \sqrt{z - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternatives

Alternative 1
Error	0.6
Cost	388

\[\begin{array}{l} \mathbf{if}\;y \leq -5.492534920634091 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	30.2
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023099 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B"
  :precision binary64

  :herbie-target
  (if (< y 2.5816096488251695e-278) (- (* x y)) (* x (* (sqrt (+ y z)) (sqrt (- y z)))))

  (* x (sqrt (- (* y y) (* z z)))))