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

Average Error: 0.1 → 0.1

Time: 30.4s

Precision: binary64

Cost: 7360

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.1
Target	0.3
Herbie	0.1

\[\left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \]

Derivation

1. Initial program 0.1

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

2. Simplified 0.1

   \[\leadsto \color{blue}{\left(\left(x + \left(y + z\right)\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b} \]
   Proof

   [Start] 0.1	\[ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   rational.json-simplify-1 [=>] 0.1	\[ \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   rational.json-simplify-41 [=>] 0.1	\[ \left(\color{blue}{\left(x + \left(y + z\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	0.6
Cost	7752

\[\begin{array}{l} t_1 := z \cdot \log t\\ t_2 := \left(\left(x + y\right) + b \cdot a\right) - \left(t_1 - z\right)\\ \mathbf{if}\;a - 0.5 \leq -10000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a - 0.5 \leq -0.4999999999999996:\\ \;\;\;\;\left(\left(x + \left(z + y\right)\right) + -0.5 \cdot b\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	4.4
Cost	7496

\[\begin{array}{l} t_1 := \left(\left(x + y\right) + b \cdot a\right) - \left(z \cdot \log t - z\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-46}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	6.7
Cost	7240

\[\begin{array}{l} t_1 := \left(y + z \cdot \left(1 - \log t\right)\right) + x\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+174}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	6.7
Cost	7240

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;\left(y + z \cdot \left(1 - \log t\right)\right) + x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+174}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(z \cdot \log t - z\right)\\ \end{array} \]

Alternative 5
Error	8.7
Cost	7112

\[\begin{array}{l} t_1 := \left(z + x\right) - z \cdot \log t\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+193}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	8.5
Cost	7112

\[\begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+132}:\\ \;\;\;\;\left(z + x\right) - t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+174}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) - t_1\\ \end{array} \]

Alternative 7
Error	9.7
Cost	6984

\[\begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+199}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	25.6
Cost	1096

\[\begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+139}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	37.7
Cost	724

\[\begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-284}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-252}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+50}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;y \leq 9.1 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10
Error	29.0
Cost	716

\[\begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+172}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{elif}\;b \leq -1.72 \cdot 10^{-152}:\\ \;\;\;\;b \cdot a + x\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+61}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b + x\\ \end{array} \]

Alternative 11
Error	21.0
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 1.46 \cdot 10^{+99}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b + y\\ \end{array} \]

Alternative 12
Error	19.4
Cost	580

\[\begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;y \leq 1.26 \cdot 10^{+94}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \]

Alternative 13
Error	15.4
Cost	576

\[\left(y + x\right) + \left(a - 0.5\right) \cdot b \]

Alternative 14
Error	29.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+173}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+137}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \]

Alternative 15
Error	37.1
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16
Error	48.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))