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

Average Error: 0.1 → 0.1

Time: 11.0s

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	6.6
Cost	13512

\[\begin{array}{l} t_1 := \log t + \left(x \cdot \log y - z\right)\\ \mathbf{if}\;x \leq -2.261404597977201 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.191480651188808 \cdot 10^{+83}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	34.7
Cost	7912

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -6.415301983820407 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7059870816866355 \cdot 10^{-5}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.350305810631241 \cdot 10^{-25}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -4.226420299713934 \cdot 10^{-41}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq -1.1113134890164492 \cdot 10^{-290}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 4.001065192217184 \cdot 10^{-267}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.965744243032282 \cdot 10^{-244}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 4.4029899575007015 \cdot 10^{-197}:\\ \;\;\;\;y - z\\ \mathbf{elif}\;x \leq 8.164223165411411 \cdot 10^{-7}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 5.368561610567112 \cdot 10^{+192}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	34.3
Cost	7388

\[\begin{array}{l} \mathbf{if}\;z \leq -7.470159941709671 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -4.146731920389646 \cdot 10^{-89}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -1.6852502626636778 \cdot 10^{-137}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq -3.0894365090748594 \cdot 10^{-217}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -5.946048270717707 \cdot 10^{-266}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 9.575177735515063 \cdot 10^{-203}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 7.183965880350874 \cdot 10^{-137}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 7.50035277431111 \cdot 10^{+81}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;y - z\\ \end{array} \]

Alternative 4
Error	25.8
Cost	7252

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -7.470159941709671 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 5.430179332096134 \cdot 10^{-18}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 2.514114965436963 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.764459183665156 \cdot 10^{+74}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 8.313665891363955 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5
Error	26.5
Cost	7252

\[\begin{array}{l} t_1 := \log t - z\\ t_2 := x \cdot \log y\\ t_3 := \log t - y\\ \mathbf{if}\;x \leq -3618579072759186000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.1113134890164492 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.404521794597546 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.499481573088827 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.368561610567112 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	10.7
Cost	6984

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -4.8557743168134363 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.368561610567112 \cdot 10^{+192}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	33.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -7.470159941709671 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 7.50035277431111 \cdot 10^{+81}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;y - z\\ \end{array} \]

Alternative 8
Error	33.4
Cost	392

\[\begin{array}{l} \mathbf{if}\;z \leq -7.470159941709671 \cdot 10^{+43}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 7.50035277431111 \cdot 10^{+81}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9
Error	45.2
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2022317 
(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)))