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

Average Error: 0.1 → 0.1

Time: 6.3s

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	6.6
Cost	13512

\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \log t - \left(y + z\right)\\ t_3 := t_1 - z\\ \mathbf{if}\;z \leq -5 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;\left(t_1 + \log t\right) - y\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	33.6
Cost	7780

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-94}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-267}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 10^{-156}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-42}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+44}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	26.1
Cost	7648

\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \log t - z\\ t_3 := \log t - y\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-94}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-284}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{+48}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	26.2
Cost	7384

\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -1.82 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-94}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	10.6
Cost	6984

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+159}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	7.3
Cost	6984

\[\begin{array}{l} t_1 := \log y \cdot x - y\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 155:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	6.7
Cost	6984

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+24}:\\ \;\;\;\;t_1 - y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \]

Alternative 8
Error	35.9
Cost	6860

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+159}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-264}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-17}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+41}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+150}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9
Error	34.3
Cost	656

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+159}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+67}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+150}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 10
Error	44.7
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023063 
(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)))