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

Average Error: 0.1 → 0.1

Time: 14.2s

Precision: binary64

Cost: 7488

Math

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

↓

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

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) (- (* a b) (* z (log t)))) z) (* 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) + ((a * b) - (z * log(t)))) + z) - (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) + ((a * b) - (z * log(t)))) + z) - (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) + ((a * b) - (z * Math.log(t)))) + z) - (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) + ((a * b) - (z * math.log(t)))) + z) - (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) + Float64(Float64(a * b) - Float64(z * log(t)))) + z) - Float64(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) + ((a * b) - (z * log(t)))) + z) - (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] + N[(N[(a * b), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] - N[(0.5 * b), $MachinePrecision]), $MachinePrecision]

Target

Original	0.1
Target	0.4
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

   \[\leadsto \color{blue}{z + \left(\left(\left(x + y\right) + \left(a - 0.5\right) \cdot b\right) - z \cdot \log t\right)} \]
   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_best_oopsla_all_46_json_45_simplify-35 [=>] 0.1	\[ \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-107 [=>] 0.1	\[ \left(a - 0.5\right) \cdot b + \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-82 [=>] 0.1	\[ \color{blue}{z + \left(\left(a - 0.5\right) \cdot b + \left(\left(x + y\right) - z \cdot \log t\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-108 [=>] 0.1	\[ z + \color{blue}{\left(\left(\left(x + y\right) + \left(a - 0.5\right) \cdot b\right) - z \cdot \log t\right)} \]

3. Applied egg-rr 0.1

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

4. Final simplification 0.1

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

Alternatives

Alternative 1
Error	7.5
Cost	8268

\[\begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := \left(y + x\right) + t_1\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+54}:\\ \;\;\;\;z + \left(\left(y + x\right) - z \cdot \log t\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z + t_1\\ \end{array} \]

Alternative 2
Error	0.1
Cost	7360

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

Alternative 3
Error	0.1
Cost	7360

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

Alternative 4
Error	6.5
Cost	7240

\[\begin{array}{l} t_1 := z + \left(\left(y + x\right) - z \cdot \log t\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+47}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	10.4
Cost	6984

\[\begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+209}:\\ \;\;\;\;\left(y + x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	43.4
Cost	1644

\[\begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+131}:\\ \;\;\;\;b \cdot -0.5\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-91}:\\ \;\;\;\;y\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-247}:\\ \;\;\;\;y\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 10^{-108}:\\ \;\;\;\;y\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+167}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot -0.5\\ \end{array} \]

Alternative 7
Error	42.8
Cost	848

\[\begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	27.0
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+22}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y - 0.5 \cdot b\\ \end{array} \]

Alternative 9
Error	25.5
Cost	580

\[\begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;y \leq 6.5 \cdot 10^{+21}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \]

Alternative 10
Error	15.3
Cost	576

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

Alternative 11
Error	36.2
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+22}:\\ \;\;\;\;x - 0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12
Error	34.8
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+22}:\\ \;\;\;\;x - 0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y - 0.5 \cdot b\\ \end{array} \]

Alternative 13
Error	43.6
Cost	196

\[\begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14
Error	48.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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)))