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

Average Error: 0.1 → 0.1

Time: 23.1s

Precision: binary64

Cost: 14016

Math

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

↓

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

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	2.2
Cost	14152

\[\begin{array}{l} t_1 := \log c \cdot b\\ \mathbf{if}\;x \leq -1 \cdot 10^{+79}:\\ \;\;\;\;\left(\left(\left(\log y \cdot x + z\right) + a\right) + t_1\right) + y \cdot i\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;\left(\left(\left(t + z\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + t_1\right) + y \cdot i\\ \end{array} \]

Alternative 2
Error	4.7
Cost	14024

\[\begin{array}{l} t_1 := \left(\left(\left(\log y \cdot x + z\right) + a\right) + \log c \cdot b\right) + y \cdot i\\ \mathbf{if}\;x \leq -1 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;\left(\left(\left(t + z\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	31.9
Cost	7768

\[\begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c + a\\ t_2 := \log y \cdot x\\ t_3 := \left(a + t_2\right) + y \cdot i\\ t_4 := \left(t_2 + z\right) + y \cdot i\\ \mathbf{if}\;z \leq -8 \cdot 10^{+132}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+36}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	8.0
Cost	7752

\[\begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+199}:\\ \;\;\;\;\left(t_1 + z\right) + y \cdot i\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\left(\log y \cdot x + \left(a + \left(t + z\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(a + t_1\right) + y \cdot i\\ \end{array} \]

Alternative 5
Error	18.4
Cost	7624

\[\begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+199}:\\ \;\;\;\;\left(t_1 + z\right) + y \cdot i\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\left(\log y \cdot x + \left(a + z\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(a + t_1\right) + y \cdot i\\ \end{array} \]

Alternative 6
Error	5.9
Cost	7624

\[\begin{array}{l} t_1 := \left(\log y \cdot x + \left(a + z\right)\right) + y \cdot i\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+82}:\\ \;\;\;\;\left(\left(\left(t + z\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	29.9
Cost	7500

\[\begin{array}{l} t_1 := \left(a + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\\ t_2 := \left(\log y \cdot x + z\right) + y \cdot i\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	29.9
Cost	7500

\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+132}:\\ \;\;\;\;\left(t_1 + z\right) + y \cdot i\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;\left(a + t_1\right) + y \cdot i\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+38}:\\ \;\;\;\;\left(t_2 + z\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(a + t_2\right) + y \cdot i\\ \end{array} \]

Alternative 9
Error	15.6
Cost	7496

\[\begin{array}{l} t_1 := \left(\log y \cdot x + \left(a + z\right)\right) + y \cdot i\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;\left(\left(b - 0.5\right) \cdot \log c + \left(a + z\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	26.1
Cost	7376

\[\begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+180}:\\ \;\;\;\;\log c \cdot b + y \cdot i\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-82}:\\ \;\;\;\;\left(a + \left(t + z\right)\right) + y \cdot i\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-193}:\\ \;\;\;\;\left(a + \log y \cdot x\right) + y \cdot i\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+151}:\\ \;\;\;\;\left(a + z\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(b - 0.5\right) \cdot \log c + a\\ \end{array} \]

Alternative 11
Error	18.8
Cost	7368

\[\begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+181}:\\ \;\;\;\;\log c \cdot b + y \cdot i\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+150}:\\ \;\;\;\;\left(a + \left(t + z\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(b - 0.5\right) \cdot \log c + a\\ \end{array} \]

Alternative 12
Error	19.0
Cost	7112

\[\begin{array}{l} t_1 := \log c \cdot b + y \cdot i\\ \mathbf{if}\;b \leq -1.32 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+186}:\\ \;\;\;\;\left(a + \left(t + z\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	19.5
Cost	6856

\[\begin{array}{l} t_1 := \log c \cdot b\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+186}:\\ \;\;\;\;\left(a + \left(t + z\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	41.7
Cost	716

\[\begin{array}{l} t_1 := a + y \cdot i\\ t_2 := z + y \cdot i\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	23.7
Cost	576

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

Alternative 16
Error	34.9
Cost	448

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

Alternative 17
Error	51.6
Cost	324

\[\begin{array}{l} \mathbf{if}\;a \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 18
Error	45.3
Cost	320

\[a + y \cdot i \]

Alternative 19
Error	52.1
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023090 
(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)))