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

Average Error: 1.5 → 0.9

Time: 5.2s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{if}\;y \leq -2.763118437090793 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{+40}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (/ (- a t) (- z t))))))
   (if (<= y -2.763118437090793e-294)
     t_1
     (if (<= y 1e+40) (+ x (/ (* y (- z t)) (- 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 / ((a - t) / (z - t)));
	double tmp;
	if (y <= -2.763118437090793e-294) {
		tmp = t_1;
	} else if (y <= 1e+40) {
		tmp = x + ((y * (z - t)) / (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 / ((a - t) / (z - t)))
    if (y <= (-2.763118437090793d-294)) then
        tmp = t_1
    else if (y <= 1d+40) then
        tmp = x + ((y * (z - t)) / (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 / ((a - t) / (z - t)));
	double tmp;
	if (y <= -2.763118437090793e-294) {
		tmp = t_1;
	} else if (y <= 1e+40) {
		tmp = x + ((y * (z - t)) / (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 / ((a - t) / (z - t)))
	tmp = 0
	if y <= -2.763118437090793e-294:
		tmp = t_1
	elif y <= 1e+40:
		tmp = x + ((y * (z - t)) / (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(a - t) / Float64(z - t))))
	tmp = 0.0
	if (y <= -2.763118437090793e-294)
		tmp = t_1;
	elseif (y <= 1e+40)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / 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 / ((a - t) / (z - t)));
	tmp = 0.0;
	if (y <= -2.763118437090793e-294)
		tmp = t_1;
	elseif (y <= 1e+40)
		tmp = x + ((y * (z - t)) / (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[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.763118437090793e-294], t$95$1, If[LessEqual[y, 1e+40], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	1.5
Target	0.4
Herbie	0.9

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

Derivation

1. Split input into 2 regimes

2. if y < -2.76311843709079307e-294 or 1.00000000000000003e40 < y

   1. Initial program 1.2

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

   2. Applied egg-rr 1.1

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

   if -2.76311843709079307e-294 < y < 1.00000000000000003e40

   1. Initial program 2.2

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

   2. Taylor expanded in y around 0 0.6

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.763118437090793 \cdot 10^{-294}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 10^{+40}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022182 
(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)))))