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

Average Error: 0.1 → 0.1

Time: 15.5s

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	8.4
Cost	13512

\[\begin{array}{l} t_1 := \left(\log y \cdot x + \log t\right) - y\\ \mathbf{if}\;x \leq -2 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+129}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.1
Cost	13512

\[\begin{array}{l} t_1 := \log y \cdot x + \log t\\ \mathbf{if}\;x \leq -2 \cdot 10^{+174}:\\ \;\;\;\;t_1 - y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+101}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \]

Alternative 3
Error	34.9
Cost	7516

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -75000000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-262}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+73}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	26.8
Cost	7384

\[\begin{array}{l} t_1 := \log t - y\\ t_2 := \log y \cdot x\\ t_3 := \log t - z\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -270000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	28.4
Cost	7252

\[\begin{array}{l} t_1 := \log t - y\\ t_2 := \log y \cdot x\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -26000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	10.3
Cost	6984

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	33.9
Cost	6860

\[\begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+74}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-147}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-278}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 75000000000000:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8
Error	33.4
Cost	392

\[\begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9
Error	44.6
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023077 
(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)))