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

Average Error: 0.1 → 0.1

Time: 19.4s

Precision: binary64

Cost: 7360

Math

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

↓

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

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(Float64(x + 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[(N[(x + y), $MachinePrecision] + z), $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. Final simplification 0.1

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

Alternatives

Alternative 1
Error	0.1
Cost	7360

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

Alternative 2
Error	6.3
Cost	7240

\[\begin{array}{l} t_1 := y + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	6.3
Cost	7240

\[\begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+95}:\\ \;\;\;\;y + \left(\left(z + x\right) - t_1\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+63}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + x\right)\right) - t_1\\ \end{array} \]

Alternative 4
Error	9.6
Cost	7112

\[\begin{array}{l} t_1 := y + \left(z - \log t \cdot z\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+63}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	9.6
Cost	7112

\[\begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+99}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z + y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - \log t \cdot z\right)\\ \end{array} \]

Alternative 6
Error	9.6
Cost	7112

\[\begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+100}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z + y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+63}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) - \log t \cdot z\\ \end{array} \]

Alternative 7
Error	9.4
Cost	6984

\[\begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -6 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+185}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	25.3
Cost	1096

\[\begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+201}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	43.9
Cost	724

\[\begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-199}:\\ \;\;\;\;b \cdot -0.5\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-103}:\\ \;\;\;\;b \cdot -0.5\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10
Error	25.9
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 245000000:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Error	25.3
Cost	580

\[\begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;y \leq 9.5 \cdot 10^{+108}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \]

Alternative 12
Error	15.4
Cost	576

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

Alternative 13
Error	30.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+224}:\\ \;\;\;\;b \cdot -0.5\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot -0.5\\ \end{array} \]

Alternative 14
Error	43.0
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 2.35 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15
Error	47.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(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)))