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

Average Error: 0.1 → 0.1

Time: 14.8s

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	6.7
Cost	13644

\[\begin{array}{l} t_1 := \left(\log t - z\right) - y\\ t_2 := \log t + x \cdot \log y\\ \mathbf{if}\;y \leq 9.944181197817244 \cdot 10^{+38}:\\ \;\;\;\;t_2 - z\\ \mathbf{elif}\;y \leq 1.041348551263286 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3541349507710127 \cdot 10^{+189}:\\ \;\;\;\;t_2 - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	6.9
Cost	13512

\[\begin{array}{l} t_1 := \left(\log t + x \cdot \log y\right) - y\\ \mathbf{if}\;x \leq -4.383177465251753 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 16488101517471.346:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	11.1
Cost	7248

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(\log t - z\right) - y\\ \mathbf{if}\;x \leq -5.9659622739583086 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 16488101517471.346:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.794675320084512 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.255695519047053 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	11.1
Cost	7248

\[\begin{array}{l} t_1 := \left(\log t - z\right) - y\\ t_2 := x \cdot \log y\\ \mathbf{if}\;x \leq -5.9659622739583086 \cdot 10^{+110}:\\ \;\;\;\;\log \left(\frac{1}{y}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 16488101517471.346:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.794675320084512 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.255695519047053 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	25.1
Cost	7120

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - z\\ \mathbf{if}\;x \leq -4.383177465251753 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.242086255228189 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.7964596990709705 \cdot 10^{-208}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 16488101517471.346:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	25.6
Cost	6856

\[\begin{array}{l} \mathbf{if}\;z \leq -1.618000456610213 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.125088476625672 \cdot 10^{+37}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7
Error	33.5
Cost	6728

\[\begin{array}{l} \mathbf{if}\;y \leq 8.178180006118397 \cdot 10^{-32}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.312947539143678 \cdot 10^{-23}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 1.0976557215818638 \cdot 10^{+96}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 8
Error	33.4
Cost	392

\[\begin{array}{l} \mathbf{if}\;z \leq -1.618000456610213 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.125088476625672 \cdot 10^{+37}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9
Error	45.2
Cost	128

\[-z \]

Reproduce

herbie shell --seed 2022316 
(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)))