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

Average Error: 0.1 → 0.1

Time: 15.1s

Precision: binary64

Cost: 1088

Math

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

↓

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

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) (- c (/ (* 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;
}

↓

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

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) + (c - ((a * b) / 4.0d0)))
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) + (c - ((a * b) / 4.0)));
}

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) + (c - ((a * b) / 4.0)))

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(x * y) + Float64(Float64(Float64(z * t) / 16.0) + Float64(c - Float64(Float64(a * b) / 4.0))))
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) + (c - ((a * b) / 4.0)));
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[(x * y), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision] + N[(c - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. Simplified 0.1

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

   [Start] 0.1	\[ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   rational_best_oopsla_all_46_json_45_simplify-35 [=>] 0.1	\[ \color{blue}{c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-35 [=>] 0.1	\[ c + \left(\color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \frac{a \cdot b}{4}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-107 [=>] 0.1	\[ c + \color{blue}{\left(x \cdot y + \left(\frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-82 [=>] 0.1	\[ \color{blue}{x \cdot y + \left(c + \left(\frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-108 [=>] 0.1	\[ x \cdot y + \color{blue}{\left(\left(\frac{z \cdot t}{16} + c\right) - \frac{a \cdot b}{4}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-35 [<=] 0.1	\[ x \cdot y + \left(\color{blue}{\left(c + \frac{z \cdot t}{16}\right)} - \frac{a \cdot b}{4}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-107 [=>] 0.1	\[ x \cdot y + \color{blue}{\left(\frac{z \cdot t}{16} + \left(c - \frac{a \cdot b}{4}\right)\right)} \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	27.0
Cost	2292

\[\begin{array}{l} t_1 := x \cdot y + c\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ t_3 := x \cdot y + t_2\\ t_4 := t_2 + c\\ t_5 := x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ t_6 := c - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{-130}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-248}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2300:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+95}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+125}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 9.1 \cdot 10^{+139}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+175}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 2
Error	25.5
Cost	2028

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := c - 0.25 \cdot \left(a \cdot b\right)\\ t_3 := x \cdot y + c\\ t_4 := t_1 + c\\ t_5 := x \cdot y + t_1\\ \mathbf{if}\;b \leq -2.85 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-247}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-294}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-263}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7.3 \cdot 10^{-68}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1900:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+47}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+175}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	9.1
Cost	1744

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := x \cdot y + \left(c + t_1\right)\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+158}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -1000000:\\ \;\;\;\;t_1 - b \cdot \left(0.25 \cdot a\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 4
Error	30.8
Cost	1640

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ t_2 := x \cdot y + c\\ t_3 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.85 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-248}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-46}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	35.3
Cost	1508

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+95}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-281}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 6
Error	24.2
Cost	1504

\[\begin{array}{l} t_1 := x \cdot y + c\\ t_2 := 0.0625 \cdot \left(t \cdot z\right) + c\\ t_3 := c - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 13200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	8.1
Cost	1224

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+158}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+126}:\\ \;\;\;\;x \cdot y + \left(c + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 8
Error	5.5
Cost	1224

\[\begin{array}{l} t_1 := \left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot y + \left(c + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	7.1
Cost	1224

\[\begin{array}{l} t_1 := 0.25 \cdot \left(a \cdot b\right)\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;c \leq -430:\\ \;\;\;\;\left(c + y \cdot x\right) - t_1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-97}:\\ \;\;\;\;\left(y \cdot x + t_2\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(c + t_2\right)\\ \end{array} \]

Alternative 10
Error	34.7
Cost	1112

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;c \leq -4.1 \cdot 10^{-12}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-284}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-174}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 11
Error	20.4
Cost	968

\[\begin{array}{l} t_1 := x \cdot y + c\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+83}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	34.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{-10}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+59}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 13
Error	43.2
Cost	64

\[c \]

Reproduce

herbie shell --seed 2023090 
(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))