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

Average Error: 1.2 → 0.5

Time: 16.1s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-89} \lor \neg \left(y \leq 5 \cdot 10^{-25}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5e-89) (not (<= y 5e-25)))
   (+ x (* y (/ (- z t) (- z a))))
   (+ x (/ (* y (- z t)) (- z a)))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-89) || !(y <= 5e-25)) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

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) / (z - a)))
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
    real(8) :: tmp
    if ((y <= (-5d-89)) .or. (.not. (y <= 5d-25))) then
        tmp = x + (y * ((z - t) / (z - a)))
    else
        tmp = x + ((y * (z - t)) / (z - a))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-89) || !(y <= 5e-25)) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5e-89) or not (y <= 5e-25):
		tmp = x + (y * ((z - t) / (z - a)))
	else:
		tmp = x + ((y * (z - t)) / (z - a))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5e-89) || !(y <= 5e-25))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5e-89) || ~((y <= 5e-25)))
		tmp = x + (y * ((z - t) / (z - a)));
	else
		tmp = x + ((y * (z - t)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5e-89], N[Not[LessEqual[y, 5e-25]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	1.2
Target	1.1
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999967e-89 or 4.99999999999999962e-25 < y

   1. Initial program 0.7

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

   if -4.99999999999999967e-89 < y < 4.99999999999999962e-25

   1. Initial program 1.9

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

   2. Simplified 0.3

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

      [Start] 1.9	\[ x + y \cdot \frac{z - t}{z - a} \]
      associate-*r/ [=>] 0.3	\[ x + \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-89} \lor \neg \left(y \leq 5 \cdot 10^{-25}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Error	17.5
Cost	1633

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{+105}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq -20:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-93}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-68} \lor \neg \left(x \leq 2800000\right) \land x \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 2
Error	12.9
Cost	1368

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z - a}{z}}\\ t_2 := x + \frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 0.108:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+225}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3
Error	15.3
Cost	1104

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+135}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 4
Error	12.5
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-33}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{+110}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	13.6
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6
Error	12.8
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-32}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 7
Error	17.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-201}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-32}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 8
Error	20.4
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -0.058:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-183}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	20.4
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-183}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	13.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-7}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-32}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Error	16.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 12
Error	13.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-5}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13
Error	1.2
Cost	704

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

Alternative 14
Error	30.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-209}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-287}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-70}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	20.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{+124}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	28.8
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, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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