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

Average Error: 0.1 → 0.1

Time: 9.2s

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	26.7
Cost	7912

\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \log t - z\\ t_3 := \log t - y\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1500000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+56}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	19.3
Cost	7908

\[\begin{array}{l} t_1 := \log t - z\\ t_2 := \log y \cdot x\\ t_3 := t_2 - y\\ t_4 := t_2 - z\\ t_5 := \log t - y\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+89}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -520:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.35 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-252}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-101}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+177}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	33.6
Cost	7648

\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+136}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -500000000000:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-107}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+57}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	26.9
Cost	7648

\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-127}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	19.3
Cost	7512

\[\begin{array}{l} t_1 := \log t - y\\ t_2 := \log y \cdot x - y\\ t_3 := \log t - z\\ \mathbf{if}\;x \leq -38:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-130}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-283}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	7.6
Cost	7248

\[\begin{array}{l} t_1 := \left(\log t - y\right) - z\\ t_2 := \log y \cdot x - z\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	33.8
Cost	6860

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-105}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-301}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8
Error	32.7
Cost	392

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+34}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+85}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9
Error	44.1
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023090 
(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)))