Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2

Average Error: 7.4 → 0.1

Time: 18.4s

Precision: binary64

Cost: 13696

Math

\[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

↓

\[\left(\mathsf{log1p}\left(-y\right) \cdot \left(z + -1\right) - t\right) + \log y \cdot \left(-1 + x\right) \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))

↓

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (log1p (- y)) (+ z -1.0)) t) (* (log y) (+ -1.0 x))))

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
}

↓

double code(double x, double y, double z, double t) {
	return ((log1p(-y) * (z + -1.0)) - t) + (log(y) * (-1.0 + x));
}

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)))) - t;
}

↓

public static double code(double x, double y, double z, double t) {
	return ((Math.log1p(-y) * (z + -1.0)) - t) + (Math.log(y) * (-1.0 + x));
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))) - t

↓

def code(x, y, z, t):
	return ((math.log1p(-y) * (z + -1.0)) - t) + (math.log(y) * (-1.0 + x))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y)))) - t)
end

↓

function code(x, y, z, t)
	return Float64(Float64(Float64(log1p(Float64(-y)) * Float64(z + -1.0)) - t) + Float64(log(y) * Float64(-1.0 + x)))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(N[(N[(N[Log[1 + (-y)], $MachinePrecision] * N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 7.4

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\left(\mathsf{log1p}\left(-y\right) \cdot \left(z + -1\right) - t\right) + \left(x + -1\right) \cdot \log y} \]

3. Final simplification 0.1

   \[\leadsto \left(\mathsf{log1p}\left(-y\right) \cdot \left(z + -1\right) - t\right) + \log y \cdot \left(-1 + x\right) \]

Alternatives

Alternative 1
Error	0.4
Cost	7616

\[\left(\log y \cdot \left(-1 + x\right) + \left(y \cdot \left(y \cdot -0.5\right) - y\right) \cdot \left(z + -1\right)\right) - t \]

Alternative 2
Error	2.8
Cost	7497

\[\begin{array}{l} \mathbf{if}\;-1 + x \leq -400000 \lor \neg \left(-1 + x \leq -1\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - y \cdot z\right) - \log y\right) - t\\ \end{array} \]

Alternative 3
Error	6.7
Cost	7241

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+183} \lor \neg \left(z \leq 1.3 \cdot 10^{+233}\right):\\ \;\;\;\;y \cdot \left(1 - z\right) + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \]

Alternative 4
Error	6.7
Cost	7241

\[\begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+183} \lor \neg \left(z \leq 1.22 \cdot 10^{+231}\right):\\ \;\;\;\;y \cdot \left(1 - z\right) + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(y + \log y \cdot \left(-1 + x\right)\right) - t\\ \end{array} \]

Alternative 5
Error	1.1
Cost	7241

\[\begin{array}{l} \mathbf{if}\;x \leq -1700 \lor \neg \left(x \leq 0.28\right):\\ \;\;\;\;x \cdot \log y - \left(t + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - y \cdot z\right) - \log y\right) - t\\ \end{array} \]

Alternative 6
Error	0.6
Cost	7232

\[\left(\log y \cdot \left(-1 + x\right) + y \cdot \left(1 - z\right)\right) - t \]

Alternative 7
Error	0.6
Cost	7232

\[\log y \cdot \left(-1 + x\right) + \left(y \cdot \left(1 - z\right) - t\right) \]

Alternative 8
Error	9.7
Cost	7113

\[\begin{array}{l} \mathbf{if}\;y \leq 2.65 \cdot 10^{-89} \lor \neg \left(y \leq 4.6 \cdot 10^{-62}\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot z\right) - t\\ \end{array} \]

Alternative 9
Error	14.4
Cost	7049

\[\begin{array}{l} \mathbf{if}\;x \leq -7900 \lor \neg \left(x \leq 6.6\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(-y\right) \cdot z - t\\ \end{array} \]

Alternative 10
Error	14.5
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -22500 \lor \neg \left(x \leq 9.5\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot z\right) - t\\ \end{array} \]

Alternative 11
Error	21.2
Cost	6857

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+69} \lor \neg \left(x \leq 1.6 \cdot 10^{+93}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(y - y \cdot z\right) - t\\ \end{array} \]

Alternative 12
Error	36.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-8}:\\ \;\;\;\;y - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 13
Error	36.2
Cost	520

\[\begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 14
Error	33.4
Cost	448

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

Alternative 15
Error	33.6
Cost	384

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

Alternative 16
Error	40.7
Cost	128

\[-t \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z t)
  :name "Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2"
  :precision binary64
  (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))