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

Average Error: 0.1 → 0.1

Time: 12.0s

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	6.9
Cost	13380

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t_1 - y\\ \mathbf{if}\;y \leq 556578173201522800:\\ \;\;\;\;\left(\log t + t_1\right) - z\\ \mathbf{elif}\;y \leq 6.537092653243584 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5336624499603674 \cdot 10^{+182}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	36.0
Cost	7648

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.720528742747759 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.568045038199247 \cdot 10^{-28}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -1.6584844398438456 \cdot 10^{-152}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 2.2222777494360173 \cdot 10^{-191}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 4.865272799055035 \cdot 10^{-160}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 9.248134250635205 \cdot 10^{-150}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.0422922649483412 \cdot 10^{-98}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.859836357188378 \cdot 10^{+188}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	20.6
Cost	7248

\[\begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y - z\\ \mathbf{if}\;x \leq -2.7232425456921666 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.248134250635205 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.0422922649483412 \cdot 10^{-98}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 4.807853983359746 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	20.4
Cost	7248

\[\begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.7232425456921666 \cdot 10^{+24}:\\ \;\;\;\;t_2 - z\\ \mathbf{elif}\;x \leq 9.248134250635205 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.0422922649483412 \cdot 10^{-98}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.4117651506705518 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - y\\ \end{array} \]

Alternative 5
Error	27.6
Cost	7120

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -2.720528742747759 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.248134250635205 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.0422922649483412 \cdot 10^{-98}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.859836357188378 \cdot 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	26.0
Cost	6988

\[\begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;y \leq 1.839854485588543 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.203655305432292 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 556578173201522800:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 7
Error	7.0
Cost	6984

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.720528742747759 \cdot 10^{+95}:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;x \leq 2.5167509035584944 \cdot 10^{+64}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \]

Alternative 8
Error	34.9
Cost	6728

\[\begin{array}{l} \mathbf{if}\;y \leq 3.1209712169990575 \cdot 10^{-265}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.0579909827475675 \cdot 10^{-113}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 556578173201522800:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9
Error	32.4
Cost	260

\[\begin{array}{l} \mathbf{if}\;y \leq 556578173201522800:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10
Error	44.6
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2022300 
(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)))