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

Average Error: 0.1 → 0.1

Time: 13.2s

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	1.4
Cost	20425

\[\begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+34} \lor \neg \left(t_1 \leq 4 \cdot 10^{-45}\right):\\ \;\;\;\;t_1 - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 2
Error	0.5
Cost	13513

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -3 \cdot 10^{+15} \lor \neg \left(z \leq 2.7 \cdot 10^{-9}\right):\\ \;\;\;\;\left(t_1 - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t_1\right) - y\\ \end{array} \]

Alternative 3
Error	19.8
Cost	7384

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-y\right) - z\\ t_3 := \log t - y\\ \mathbf{if}\;z \leq -3 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	19.9
Cost	7256

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-y\right) - z\\ t_3 := \log t - y\\ \mathbf{if}\;z \leq -3 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-13}:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	10.1
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+149} \lor \neg \left(x \leq 1.5 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 6
Error	6.8
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+44} \lor \neg \left(x \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 7
Error	18.1
Cost	6857

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+149} \lor \neg \left(x \leq 7.2 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]

Alternative 8
Error	27.0
Cost	6729

\[\begin{array}{l} \mathbf{if}\;z \leq 1.22 \cdot 10^{-144} \lor \neg \left(z \leq 6.5 \cdot 10^{-14}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t\\ \end{array} \]

Alternative 9
Error	32.3
Cost	260

\[\begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10
Error	26.2
Cost	256

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

Alternative 11
Error	44.8
Cost	128

\[-y \]

Alternative 12
Error	62.5
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023023 
(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)))