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

Average Error: 0.19% → 0.19%

Time: 11.9s

Precision: binary64

Cost: 1088

Math

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

↓

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

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
 (+ (- (+ (/ (* z t) 16.0) (* x y)) (/ (* 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 ((((z * t) / 16.0) + (x * y)) - ((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 = ((((z * t) / 16.0d0) + (x * y)) - ((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 ((((z * t) / 16.0) + (x * y)) - ((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 ((((z * t) / 16.0) + (x * y)) - ((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(Float64(z * t) / 16.0) + Float64(x * y)) - 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 = ((((z * t) / 16.0) + (x * y)) - ((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[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 0.19

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

2. Final simplification 0.19

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

Alternatives

Alternative 1
Error	58.57%
Cost	2660

\[\begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -2300000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.3 \cdot 10^{-251}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 1.35 \cdot 10^{-183}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 4.7 \cdot 10^{-91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4.6 \cdot 10^{+63}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	35.97%
Cost	1504

\[\begin{array}{l} t_1 := x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -4.6 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -0.00385:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1060:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	55.6%
Cost	1380

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -6.4 \cdot 10^{+58}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{+29}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \leq -3.2:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-302}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 4
Error	8.84%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+15} \lor \neg \left(a \cdot b \leq 10^{+25}\right):\\ \;\;\;\;x \cdot y + \left(c - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 5
Error	13.22%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+115}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+63}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 6
Error	32.37%
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+22} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+86}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 7
Error	36.96%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+109} \lor \neg \left(a \cdot b \leq 4.8 \cdot 10^{+158}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 8
Error	55.73%
Cost	456

\[\begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+59}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+18}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 9
Error	68.37%
Cost	64

\[c \]

Reproduce

herbie shell --seed 2023115 
(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))