Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Average Error: 0.1 → 0.1

Time: 24.9s

Precision: binary64

Cost: 1088

Math

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

↓

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

↓

real(8) function code(x, y, z, t, a, b, c)
    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
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

↓

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

↓

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

↓

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Final simplification 0.1

   \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

Alternatives

Alternative 1
Error	25.9
Cost	1896

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right) + c\\ t_2 := y \cdot x + t \cdot \left(0.0625 \cdot z\right)\\ t_3 := c + y \cdot x\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-222}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + c\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 995500:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+221}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	25.2
Cost	1768

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right) + c\\ t_2 := c + y \cdot x\\ t_3 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	25.2
Cost	1504

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right) + c\\ t_2 := c + y \cdot x\\ t_3 := 0.0625 \cdot \left(t \cdot z\right) + c\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+208}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	35.6
Cost	1376

\[\begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ t_2 := t \cdot \left(0.0625 \cdot z\right)\\ \mathbf{if}\;c \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-245}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-300}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-135}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 5
Error	6.4
Cost	1352

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := \left(c + t_1\right) - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 10^{-33}:\\ \;\;\;\;t_1 + \left(c + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	8.2
Cost	1224

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right) + c\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+173}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + \left(c + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	8.4
Cost	1224

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right) + c\\ \mathbf{elif}\;a \cdot b \leq 10^{+78}:\\ \;\;\;\;t_1 + \left(c + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 8
Error	35.9
Cost	984

\[\begin{array}{l} t_1 := t \cdot \left(0.0625 \cdot z\right)\\ \mathbf{if}\;c \leq -8.4 \cdot 10^{+74}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -0.00182:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-300}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+84}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 9
Error	25.0
Cost	840

\[\begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 4.3 \cdot 10^{+97}:\\ \;\;\;\;c + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	35.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+84}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 11
Error	44.0
Cost	64

\[c \]

Reproduce

herbie shell --seed 2023074 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))