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

Average Error: 1.4 → 1.6

Time: 8.8s

Precision: binary64

Cost: 1352

Math

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

↓

\[\begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-270}:\\ \;\;\;\;\frac{y \cdot z}{a - t} + \left(x - \frac{t \cdot y}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= t -3e+44)
     t_1
     (if (<= t 2.6e-270)
       (+ (/ (* y z) (- a t)) (- x (/ (* t y) (- a t))))
       t_1))))

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) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (t <= -3e+44) {
		tmp = t_1;
	} else if (t <= 2.6e-270) {
		tmp = ((y * z) / (a - t)) + (x - ((t * y) / (a - t)));
	} else {
		tmp = t_1;
	}
	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) / (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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (t <= (-3d+44)) then
        tmp = t_1
    else if (t <= 2.6d-270) then
        tmp = ((y * z) / (a - t)) + (x - ((t * y) / (a - t)))
    else
        tmp = t_1
    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) / (a - t)));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (t <= -3e+44) {
		tmp = t_1;
	} else if (t <= 2.6e-270) {
		tmp = ((y * z) / (a - t)) + (x - ((t * y) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if t <= -3e+44:
		tmp = t_1
	elif t <= 2.6e-270:
		tmp = ((y * z) / (a - t)) + (x - ((t * y) / (a - t)))
	else:
		tmp = t_1
	return tmp

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)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (t <= -3e+44)
		tmp = t_1;
	elseif (t <= 2.6e-270)
		tmp = Float64(Float64(Float64(y * z) / Float64(a - t)) + Float64(x - Float64(Float64(t * y) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (t <= -3e+44)
		tmp = t_1;
	elseif (t <= 2.6e-270)
		tmp = ((y * z) / (a - t)) + (x - ((t * y) / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
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_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+44], t$95$1, If[LessEqual[t, 2.6e-270], N[(N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(x - N[(N[(t * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	1.4
Target	0.5
Herbie	1.6

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

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999987e44 or 2.6000000000000002e-270 < t

   1. Initial program 0.9

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

   if -2.99999999999999987e44 < t < 2.6000000000000002e-270

   1. Initial program 2.6

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

   2. Taylor expanded in z around 0 3.3

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t} + \left(-1 \cdot \frac{y \cdot t}{a - t} + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-270}:\\ \;\;\;\;\frac{y \cdot z}{a - t} + \left(x - \frac{t \cdot y}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.8
Cost	1104

\[\begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-120}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+169}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	20.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-44}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 3
Error	10.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Error	14.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+105}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	1.4
Cost	704

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

Alternative 7
Error	19.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+141}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+107}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	27.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-305}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022329 
(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)))))