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

Average Error: 0.1 → 0.1

Time: 11.1s

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 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	26953

\[\begin{array}{l} t_1 := \left(x \cdot \log y - y\right) - z\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+22} \lor \neg \left(t_1 \leq 10^{-20}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{t}{e^{z}}\right) - y\\ \end{array} \]

Alternative 2
Error	0.9
Cost	20425

\[\begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+32} \lor \neg \left(t_1 \leq 10^{-20}\right):\\ \;\;\;\;t_1 - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 3
Error	18.1
Cost	7120

\[\begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-z\right) - y\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-295}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.3
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+99} \lor \neg \left(x \leq 1.92 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 5
Error	6.5
Cost	6985

\[\begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+78} \lor \neg \left(x \leq 3.2 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 6
Error	6.1
Cost	6984

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+54}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \]

Alternative 7
Error	18.0
Cost	6857

\[\begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+100} \lor \neg \left(x \leq 1.36 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 8
Error	32.8
Cost	260

\[\begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+29}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9
Error	26.8
Cost	256

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

Alternative 10
Error	44.9
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023066 
(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)))