Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Average Accuracy: 66.0% → 66.0%

Time: 12.7s

Precision: binary64

Cost: 960

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x + (y * z)) + (t * a)) + ((a * z) * b)
end function

↓

real(8) function code(x, y, z, t, a, b)
    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
    code = ((z * a) * b) + ((t * a) + (x + (y * z)))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	66.0%
Target	67.9%
Herbie	66.0%

\[\begin{array}{l} \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array} \]

Derivation

1. Initial program 65.5%

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

2. Final simplification 65.5%

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

Alternatives

Alternative 1
Accuracy	32.8%
Cost	1380

\[\begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-181}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-276}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-303}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-201}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+24}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	60.4%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-151} \lor \neg \left(x \leq 6.4 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]

Alternative 3
Accuracy	65.0%
Cost	960

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

Alternative 4
Accuracy	43.3%
Cost	848

\[\begin{array}{l} t_1 := x + y \cdot z\\ t_2 := x + t \cdot a\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	42.2%
Cost	848

\[\begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+197}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 6
Accuracy	54.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-39} \lor \neg \left(a \leq 1.05 \cdot 10^{-177}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 7
Accuracy	60.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-71} \lor \neg \left(y \leq 1.92 \cdot 10^{-56}\right):\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 8
Accuracy	33.9%
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-181}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+24}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	40.9%
Cost	717

\[\begin{array}{l} \mathbf{if}\;y \leq -95000 \lor \neg \left(y \leq 7.3 \cdot 10^{+143}\right) \land y \leq 2.1 \cdot 10^{+231}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 10
Accuracy	47.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-44} \lor \neg \left(y \leq 5.2 \cdot 10^{-65}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 11
Accuracy	33.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-107}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	26.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))