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

Average Error: 16.85% → 0.84%

Time: 46.5s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+223}:\\ \;\;\;\;\frac{y - z}{1} \cdot \frac{t}{a - z} + x\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;t \ne 0:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 -1e+223)
     (+ (* (/ (- y z) 1.0) (/ t (- a z))) x)
     (if (<= t_1 5e+306)
       (+ x t_1)
       (if (!= t 0.0)
         (+ x (/ (- y z) (/ (- a z) t)))
         (+ (/ (* t (- y z)) (- a z)) x))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+223) {
		tmp = (((y - z) / 1.0) * (t / (a - z))) + x;
	} else if (t_1 <= 5e+306) {
		tmp = x + t_1;
	} else if (t != 0.0) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = ((t * (y - z)) / (a - z)) + x;
	}
	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 - z))
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 = ((y - z) * t) / (a - z)
    if (t_1 <= (-1d+223)) then
        tmp = (((y - z) / 1.0d0) * (t / (a - z))) + x
    else if (t_1 <= 5d+306) then
        tmp = x + t_1
    else if (t /= 0.0d0) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = ((t * (y - z)) / (a - z)) + x
    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 - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+223) {
		tmp = (((y - z) / 1.0) * (t / (a - z))) + x;
	} else if (t_1 <= 5e+306) {
		tmp = x + t_1;
	} else if (t != 0.0) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = ((t * (y - z)) / (a - z)) + x;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -1e+223:
		tmp = (((y - z) / 1.0) * (t / (a - z))) + x
	elif t_1 <= 5e+306:
		tmp = x + t_1
	elif t != 0.0:
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = ((t * (y - z)) / (a - z)) + x
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -1e+223)
		tmp = Float64(Float64(Float64(Float64(y - z) / 1.0) * Float64(t / Float64(a - z))) + x);
	elseif (t_1 <= 5e+306)
		tmp = Float64(x + t_1);
	elseif (t != 0.0)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(Float64(Float64(t * Float64(y - z)) / Float64(a - z)) + x);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -1e+223)
		tmp = (((y - z) / 1.0) * (t / (a - z))) + x;
	elseif (t_1 <= 5e+306)
		tmp = x + t_1;
	elseif (t ~= 0.0)
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = ((t * (y - z)) / (a - z)) + x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+223], N[(N[(N[(N[(y - z), $MachinePrecision] / 1.0), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(x + t$95$1), $MachinePrecision], If[Unequal[t, 0.0], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

Target

Original	16.85%
Target	0.92%
Herbie	0.84%

\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -1.00000000000000005e223

   1. Initial program 78.73

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

   2. Simplified 78.73

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

   3. Applied egg-rr 5.05

      \[\leadsto \color{blue}{\frac{y - z}{1} \cdot \frac{t}{a - z}} + x \]

   if -1.00000000000000005e223 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999993e306

   1. Initial program 0.36

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

   if 4.99999999999999993e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 99.56

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

   2. Simplified 99.56

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

   3. Applied egg-rr 0.42

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;t \ne 0:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x\\ } \end{array}} \]
3. Recombined 3 regimes into one program.

Reproduce

herbie shell --seed 2023136 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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