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

Average Error: 0.1 → 0.1

Time: 32.1s

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	0.9
Cost	7112

\[\begin{array}{l} t_1 := x \cdot \log y - \left(y + z\right)\\ \mathbf{if}\;x \leq -3600000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	10.2
Cost	6984

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+167}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	7.3
Cost	6984

\[\begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -1.48 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	7.3
Cost	6984

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+121}:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+120}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \]

Alternative 5
Error	18.4
Cost	6856

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.45 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+169}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	33.2
Cost	260

\[\begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{+87}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 7
Error	26.7
Cost	256

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

Alternative 8
Error	44.8
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2022325 
(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)))