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

Average Accuracy: 99.9% → 99.9%

Time: 11.7s

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	88.9%
Cost	13645

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+147}:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;z \leq -380000 \lor \neg \left(z \leq 1.12 \cdot 10^{+24}\right):\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t_1\right) - y\\ \end{array} \]

Alternative 2
Accuracy	57.3%
Cost	7913

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -8 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-214}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-283}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-185}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 50000000000000 \lor \neg \left(x \leq 4.6 \cdot 10^{+36}\right) \land x \leq 3.3 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	89.0%
Cost	7248

\[\begin{array}{l} t_1 := \log t - \left(y + z\right)\\ t_2 := x \cdot \log y\\ t_3 := t_2 - z\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{+59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 920000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - y\\ \end{array} \]

Alternative 4
Accuracy	48.6%
Cost	7120

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.7 \cdot 10^{-112}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 125000:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 8.9 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5
Accuracy	59.5%
Cost	7120

\[\begin{array}{l} t_1 := \log t - z\\ t_2 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.75 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 98000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]

Alternative 6
Accuracy	82.8%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+198} \lor \neg \left(x \leq 1.55 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 7
Accuracy	88.9%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+88} \lor \neg \left(x \leq 1.38 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 8
Accuracy	48.7%
Cost	260

\[\begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+29}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9
Accuracy	29.9%
Cost	128

\[-y \]

Alternative 10
Accuracy	2.3%
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023137 
(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)))