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

Average Accuracy: 99.9% → 99.9%

Time: 12.1s

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 99.9%

   \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

2. Final simplification 99.9%

   \[\leadsto \left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

Alternatives

Alternative 1
Accuracy	89.4%
Cost	13644

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t + \left(t_1 - z\right)\\ \mathbf{if}\;y \leq 3 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+113}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \]

Alternative 2
Accuracy	61.1%
Cost	7252

\[\begin{array}{l} t_1 := \log t - y\\ t_2 := x \cdot \log y\\ t_3 := \log t - z\\ \mathbf{if}\;x \leq -4 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	47.3%
Cost	6988

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 2.9 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+117}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 4
Accuracy	83.4%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+186} \lor \neg \left(x \leq 1.75 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 5
Accuracy	88.7%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+120} \lor \neg \left(x \leq 2.9\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 6
Accuracy	60.7%
Cost	6856

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+88}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+44}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7
Accuracy	48.2%
Cost	392

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+93}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8
Accuracy	30.1%
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023147 
(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)))