Linear.V4:$cdot from linear-1.19.1.3, C

Average Error: 0.0 → 0.0

Time: 16.4s

Precision: binary64

Cost: 960

Math

\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

↓

\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

↓

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((x * y) + (z * t)) + (a * b)) + (c * i)
end function

↓

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((x * y) + (z * t)) + (a * b)) + (c * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((x * y) + (z * t)) + (a * b)) + (c * i)

↓

def code(x, y, z, t, a, b, c, i):
	return (((x * y) + (z * t)) + (a * b)) + (c * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

↓

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * y) + (z * t)) + (a * b)) + (c * i);
end

↓

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * y) + (z * t)) + (a * b)) + (c * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

2. Final simplification 0.0

   \[\leadsto \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

Alternatives

Alternative 1
Error	28.2
Cost	2428

\[\begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := t \cdot z + a \cdot b\\ t_3 := t \cdot z + c \cdot i\\ t_4 := y \cdot x + c \cdot i\\ t_5 := y \cdot x + a \cdot b\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+219}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{+149}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+71}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-138}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	28.1
Cost	2164

\[\begin{array}{l} t_1 := t \cdot z + c \cdot i\\ t_2 := a \cdot b + c \cdot i\\ t_3 := t \cdot z + a \cdot b\\ t_4 := y \cdot x + t \cdot z\\ t_5 := y \cdot x + a \cdot b\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+165}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{+69}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-158}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-137}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	42.8
Cost	1908

\[\begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+149}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+117}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+81}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-120}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-158}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-196}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-235}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-273}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-272}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-222}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq 2.12 \cdot 10^{-175}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-137}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4
Error	27.4
Cost	1504

\[\begin{array}{l} t_1 := t \cdot z + c \cdot i\\ t_2 := y \cdot x + a \cdot b\\ \mathbf{if}\;b \leq -5.3 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.3:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	11.2
Cost	1496

\[\begin{array}{l} t_1 := \left(y \cdot x + t \cdot z\right) + c \cdot i\\ t_2 := \left(a \cdot b + t \cdot z\right) + c \cdot i\\ \mathbf{if}\;t \leq -1.48 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+72}:\\ \;\;\;\;\left(a \cdot b + y \cdot x\right) + c \cdot i\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+261}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	22.6
Cost	1488

\[\begin{array}{l} t_1 := t \cdot z + a \cdot b\\ t_2 := t \cdot z + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -600000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq -5.4 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -3.2 \cdot 10^{-213}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \cdot i \leq 3.5 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	16.7
Cost	1232

\[\begin{array}{l} t_1 := \left(a \cdot b + t \cdot z\right) + c \cdot i\\ t_2 := y \cdot x + t \cdot z\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+81}:\\ \;\;\;\;y \cdot x + c \cdot i\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	11.9
Cost	1232

\[\begin{array}{l} t_1 := \left(a \cdot b + t \cdot z\right) + c \cdot i\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+84}:\\ \;\;\;\;y \cdot x + t \cdot z\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-122}:\\ \;\;\;\;\left(a \cdot b + y \cdot x\right) + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	33.6
Cost	976

\[\begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+242}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+85}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]

Alternative 10
Error	42.2
Cost	852

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-48}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-294}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-259}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-29}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+100}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]

Alternative 11
Error	38.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{-30}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-31}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 12
Error	26.7
Cost	712

\[\begin{array}{l} t_1 := t \cdot z + a \cdot b\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	47.5
Cost	192

\[a \cdot b \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))