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

Average Error: 10.9 → 0.6

Time: 4.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z - a}{z - t}}\\ t_2 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+154}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{z - a}\right) - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ (- z a) (- z t))))) (t_2 (/ (* y (- z t)) (- z a))))
   (if (<= t_2 -2e+295)
     t_1
     (if (<= t_2 2e+154)
       (- (+ x (/ (* y z) (- z a))) (/ (* y t) (- z a)))
       t_1))))

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 t_1 = x + (y / ((z - a) / (z - t)));
	double t_2 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_2 <= -2e+295) {
		tmp = t_1;
	} else if (t_2 <= 2e+154) {
		tmp = (x + ((y * z) / (z - a))) - ((y * t) / (z - a));
	} 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)) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / ((z - a) / (z - t)))
    t_2 = (y * (z - t)) / (z - a)
    if (t_2 <= (-2d+295)) then
        tmp = t_1
    else if (t_2 <= 2d+154) then
        tmp = (x + ((y * z) / (z - a))) - ((y * t) / (z - a))
    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)) / (z - a));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / ((z - a) / (z - t)));
	double t_2 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_2 <= -2e+295) {
		tmp = t_1;
	} else if (t_2 <= 2e+154) {
		tmp = (x + ((y * z) / (z - a))) - ((y * t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = x + (y / ((z - a) / (z - t)))
	t_2 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_2 <= -2e+295:
		tmp = t_1
	elif t_2 <= 2e+154:
		tmp = (x + ((y * z) / (z - a))) - ((y * t) / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))))
	t_2 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_2 <= -2e+295)
		tmp = t_1;
	elseif (t_2 <= 2e+154)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / Float64(z - a))) - Float64(Float64(y * t) / Float64(z - a)));
	else
		tmp = t_1;
	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)
	t_1 = x + (y / ((z - a) / (z - t)));
	t_2 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if (t_2 <= -2e+295)
		tmp = t_1;
	elseif (t_2 <= 2e+154)
		tmp = (x + ((y * z) / (z - a))) - ((y * t) / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+295], t$95$1, If[LessEqual[t$95$2, 2e+154], N[(N[(x + N[(N[(y * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Target

Original	10.9
Target	1.2
Herbie	0.6

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -2e295 or 2.00000000000000007e154 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 48.8

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

   2. Simplified 2.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]

   3. Applied egg-rr 1.9

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

   if -2e295 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000007e154

   1. Initial program 0.3

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

   2. Simplified 1.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]

   3. Taylor expanded in t around 0 0.3

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -2 \cdot 10^{+295}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+154}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{z - a}\right) - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022182 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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