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

Average Error: 0.1 → 0.1

Time: 11.2s

Precision: binary64

Cost: 13376

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * log(y)) - y) - z) + log(t)
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * log(y)) - y) - z) + log(t)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Alternatives

Alternative 1
Error	6.4
Cost	13644

\[\begin{array}{l} t_1 := \log t + x \cdot \log y\\ t_2 := t_1 - z\\ \mathbf{if}\;y \leq 5.7460494645468356 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.653593345444799 \cdot 10^{+80}:\\ \;\;\;\;t_1 - y\\ \mathbf{elif}\;y \leq 1.679265714973454 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 2
Error	6.4
Cost	13380

\[\begin{array}{l} \mathbf{if}\;y \leq 2.2977323272946146 \cdot 10^{+52}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 3
Error	19.2
Cost	7120

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-z\right) - y\\ \mathbf{if}\;x \leq -5.063455026104819 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.1998872101315033 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.199518369404411 \cdot 10^{-89}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 9.864608795944753 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.6
Cost	6984

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -5.063455026104819 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.864608795944753 \cdot 10^{+67}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	18.7
Cost	6856

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -5.063455026104819 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.864608795944753 \cdot 10^{+67}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	18.8
Cost	6724

\[\begin{array}{l} \mathbf{if}\;y \leq 2.3376409766642585 \cdot 10^{-5}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 7
Error	27.0
Cost	6596

\[\begin{array}{l} \mathbf{if}\;y \leq 2.045379419257864 \cdot 10^{-283}:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 8
Error	33.0
Cost	524

\[\begin{array}{l} \mathbf{if}\;y \leq 5.7460494645468356 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 7.524506042930274 \cdot 10^{+157}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 5.34444151642604 \cdot 10^{+170}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9
Error	26.6
Cost	256

\[\left(-z\right) - y \]

Alternative 10
Error	45.1
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))