Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Average Error: 1.3 → 1.3

Time: 10.6s

Precision: binary64

Cost: 704

Math

\[x + y \cdot \frac{z - t}{a - t} \]

↓

\[x + y \cdot \frac{z - t}{a - t} \]

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	1.3
Target	0.5
Herbie	1.3

\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Initial program 1.3

   \[x + y \cdot \frac{z - t}{a - t} \]

2. Final simplification 1.3

   \[\leadsto x + y \cdot \frac{z - t}{a - t} \]

Alternatives

Alternative 1
Error	12.3
Cost	3157

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t_1 \leq 10^{-18}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 1.00002 \lor \neg \left(t_1 \leq 10^{+31}\right) \land t_1 \leq 2 \cdot 10^{+149}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 2
Error	12.0
Cost	3157

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t_1 \leq 10^{-18}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 1.00002:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{-t}}\\ \mathbf{elif}\;t_1 \leq 10^{+31} \lor \neg \left(t_1 \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Error	12.3
Cost	3028

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+120}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t_1 \leq 10^{-18}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 1.00002:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t_1 \leq 10^{+31}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+149}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \end{array} \]

Alternative 4
Error	20.1
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-212}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-172}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	14.4
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -800000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-111}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	22.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq 1.2 \cdot 10^{-269}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	14.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -620000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-60}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	19.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9
Error	29.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-161}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	28.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

  (+ x (* y (/ (- z t) (- a t)))))