Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B

Average Error: 0.1 → 0.1

Time: 39.1s

Precision: binary64

Cost: 14016

Math

\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

↓

\[\left(\left(\left(t + \left(z + x \cdot \log y\right)\right) + a\right) + \left(b + -0.5\right) \cdot \log c\right) + y \cdot i \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

↓

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ t (+ z (* x (log y)))) a) (* (+ b -0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((t + (z + (x * log(y)))) + a) + ((b + -0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

↓

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((t + (z + (x * log(y)))) + a) + ((b + (-0.5d0)) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((t + (z + (x * Math.log(y)))) + a) + ((b + -0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

↓

def code(x, y, z, t, a, b, c, i):
	return (((t + (z + (x * math.log(y)))) + a) + ((b + -0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

↓

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(t + Float64(z + Float64(x * log(y)))) + a) + Float64(Float64(b + -0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

↓

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((t + (z + (x * log(y)))) + a) + ((b + -0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

2. Final simplification 0.1

   \[\leadsto \left(\left(\left(t + \left(z + x \cdot \log y\right)\right) + a\right) + \left(b + -0.5\right) \cdot \log c\right) + y \cdot i \]

Alternatives

Alternative 1
Error	2.9
Cost	14024

\[\begin{array}{l} t_1 := \left(b + -0.5\right) \cdot \log c\\ t_2 := x \cdot \log y + \left(a + \left(t_1 + \left(z + t\right)\right)\right)\\ \mathbf{if}\;x \leq -1.6854487543609382 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.7640069717582932 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(t_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	1.4
Cost	13888

\[y \cdot i + \left(\left(\left(t + \left(z + x \cdot \log y\right)\right) + a\right) + b \cdot \log c\right) \]

Alternative 3
Error	5.0
Cost	13764

\[\begin{array}{l} t_1 := a + \left(z + t\right)\\ t_2 := \left(b + -0.5\right) \cdot \log c\\ \mathbf{if}\;x \leq -1.6854487543609382 \cdot 10^{+162}:\\ \;\;\;\;t_2 + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{elif}\;x \leq 2.7640069717582932 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(t_2 + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, t_1\right)\\ \end{array} \]

Alternative 4
Error	5.0
Cost	13512

\[\begin{array}{l} t_1 := a + \left(z + t\right)\\ \mathbf{if}\;x \leq -1.6854487543609382 \cdot 10^{+162}:\\ \;\;\;\;t + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 2.7640069717582932 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(\left(b + -0.5\right) \cdot \log c + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, t_1\right)\\ \end{array} \]

Alternative 5
Error	17.9
Cost	7900

\[\begin{array}{l} t_1 := b \cdot \log c\\ t_2 := y \cdot i + \left(a + \left(z + t\right)\right)\\ t_3 := t + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;b \leq -1.0915640008419189 \cdot 10^{+184}:\\ \;\;\;\;y \cdot i + t_1\\ \mathbf{elif}\;b \leq -1.146077689626282 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.084123958326156 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.245167423069718 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.738576241411679 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5284587.108498984:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.4615311460090376 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t_1\right)\\ \end{array} \]

Alternative 6
Error	17.4
Cost	7900

\[\begin{array}{l} t_1 := y \cdot i + \left(a + \left(z + t\right)\right)\\ t_2 := t + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;b \leq -1.0915640008419189 \cdot 10^{+184}:\\ \;\;\;\;y \cdot i + \left(t + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;b \leq -1.146077689626282 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.084123958326156 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.245167423069718 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.738576241411679 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5284587.108498984:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.4615311460090376 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 7
Error	17.9
Cost	7768

\[\begin{array}{l} t_1 := b \cdot \log c\\ t_2 := y \cdot i + \left(a + \left(z + t\right)\right)\\ t_3 := t + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;b \leq -1.0915640008419189 \cdot 10^{+184}:\\ \;\;\;\;y \cdot i + t_1\\ \mathbf{elif}\;b \leq -1.146077689626282 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.084123958326156 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.245167423069718 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.738576241411679 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5284587.108498984:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.694410182169868 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	5.0
Cost	7624

\[\begin{array}{l} t_1 := t + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -1.6854487543609382 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7640069717582932 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(\left(b + -0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	6.2
Cost	7496

\[\begin{array}{l} t_1 := t + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -1.6854487543609382 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7640069717582932 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	17.3
Cost	7112

\[\begin{array}{l} t_1 := x \cdot \log y + \left(z + t\right)\\ \mathbf{if}\;x \leq -1.6854487543609382 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.0587657637028676 \cdot 10^{+92}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	19.5
Cost	6984

\[\begin{array}{l} t_1 := a + x \cdot \log y\\ \mathbf{if}\;x \leq -2.311337777454866 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7640069717582932 \cdot 10^{+81}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	19.0
Cost	6980

\[\begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -1.0915640008419189 \cdot 10^{+184}:\\ \;\;\;\;y \cdot i + t_1\\ \mathbf{elif}\;b \leq 3.694410182169868 \cdot 10^{+178}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	19.3
Cost	6856

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.311337777454866 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5576336468463983 \cdot 10^{+192}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	19.3
Cost	6856

\[\begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -1.0915640008419189 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.694410182169868 \cdot 10^{+178}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	23.8
Cost	576

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

Alternative 16
Error	49.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -4.685450960195517 \cdot 10^{+115}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3282217899311.8794:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17
Error	40.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -4.685450960195517 \cdot 10^{+115}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3282217899311.8794:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]

Alternative 18
Error	37.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3732914955494972 \cdot 10^{+48}:\\ \;\;\;\;t + \left(z + a\right)\\ \mathbf{elif}\;z \leq -3282217899311.8794:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]

Alternative 19
Error	40.3
Cost	452

\[\begin{array}{l} \mathbf{if}\;z \leq -4.685450960195517 \cdot 10^{+115}:\\ \;\;\;\;t + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 20
Error	48.8
Cost	196

\[\begin{array}{l} \mathbf{if}\;z \leq -4.685450960195517 \cdot 10^{+115}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 21
Error	52.7
Cost	64

\[a \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))