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

Average Error: 0.1 → 0.1

Time: 49.6s

Precision: binary64

Cost: 14016

Math

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

↓

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

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
 (+ (+ (+ (+ (+ (* x (log y)) z) t) 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 (((((x * log(y)) + z) + t) + 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 = (((((x * log(y)) + z) + t) + 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 (((((x * Math.log(y)) + z) + t) + 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 (((((x * math.log(y)) + z) + t) + 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(Float64(Float64(x * log(y)) + z) + t) + 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 = (((((x * log(y)) + z) + t) + 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[(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]

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

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

Alternatives

Alternative 1
Error	0.4
Cost	14152

\[\begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log c \cdot b\right) + y \cdot i\\ \mathbf{if}\;x \leq -2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-136}:\\ \;\;\;\;\left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	3.6
Cost	13892

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+37}:\\ \;\;\;\;\left(\log c \cdot \left(b - 0.5\right) + \left(t + z\right)\right) + \left(t_1 + a\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+43}:\\ \;\;\;\;\left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 + \left(t + \left(a + z\right)\right)\right) + y \cdot i\\ \end{array} \]

Alternative 3
Error	7.7
Cost	7752

\[\begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+211}:\\ \;\;\;\;a + t_1\\ \mathbf{elif}\;b - 0.5 \leq 10^{+134}:\\ \;\;\;\;\left(\log y \cdot x + \left(t + \left(a + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(a + z\right)\\ \end{array} \]

Alternative 4
Error	4.0
Cost	7624

\[\begin{array}{l} t_1 := \left(\log y \cdot x + \left(t + \left(a + z\right)\right)\right) + y \cdot i\\ \mathbf{if}\;x \leq -7 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;\left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	14.8
Cost	7368

\[\begin{array}{l} t_1 := \log y \cdot x + \left(a + z\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.7 \cdot 10^{+43}:\\ \;\;\;\;\left(\log c \cdot \left(b - 0.5\right) + \left(t + z\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	21.8
Cost	7244

\[\begin{array}{l} t_1 := a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.04 \cdot 10^{-237}:\\ \;\;\;\;\left(z + \left(a + t\right)\right) + y \cdot i\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+154}:\\ \;\;\;\;\log y \cdot x + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	23.0
Cost	7240

\[\begin{array}{l} t_1 := \log y \cdot x + \left(a + z\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+43}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	18.2
Cost	7112

\[\begin{array}{l} t_1 := a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;b \leq -5.3 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+155}:\\ \;\;\;\;\left(z + \left(a + t\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	19.0
Cost	6856

\[\begin{array}{l} t_1 := \log c \cdot b\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+196}:\\ \;\;\;\;\left(z + \left(a + t\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	31.8
Cost	848

\[\begin{array}{l} t_1 := t + \left(a + z\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+61}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-86}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	48.8
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+139}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-41}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-82}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12
Error	23.4
Cost	576

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

Alternative 13
Error	34.3
Cost	448

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

Alternative 14
Error	48.6
Cost	196

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+139}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15
Error	52.5
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023074 
(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)))