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

Average Error: 16.82% → 1.28%

Time: 8.2s

Precision: binary64

Cost: 1993

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq 0 \lor \neg \left(t_1 \leq 5 \cdot 10^{+270}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \]

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 (or (<= t_1 0.0) (not (<= t_1 5e+270)))
     (+ x (* (/ (- y z) (- a z)) t))
     (+ x t_1))))

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 <= 0.0) || !(t_1 <= 5e+270)) {
		tmp = x + (((y - z) / (a - z)) * t);
	} else {
		tmp = x + 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 - 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 <= 0.0d0) .or. (.not. (t_1 <= 5d+270))) then
        tmp = x + (((y - z) / (a - z)) * t)
    else
        tmp = x + 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 - 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 <= 0.0) || !(t_1 <= 5e+270)) {
		tmp = x + (((y - z) / (a - z)) * t);
	} else {
		tmp = x + t_1;
	}
	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 <= 0.0) or not (t_1 <= 5e+270):
		tmp = x + (((y - z) / (a - z)) * t)
	else:
		tmp = x + t_1
	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 <= 0.0) || !(t_1 <= 5e+270))
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t));
	else
		tmp = Float64(x + t_1);
	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 <= 0.0) || ~((t_1 <= 5e+270)))
		tmp = x + (((y - z) / (a - z)) * t);
	else
		tmp = x + t_1;
	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[Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 5e+270]], $MachinePrecision]], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Target

Original	16.82%
Target	0.9%
Herbie	1.28%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -0.0 or 4.99999999999999976e270 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 26.16

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

   2. Simplified 1.9

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

      [Start] 26.16	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 1.9	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -0.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999976e270

   1. Initial program 0.19

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

4. Final simplification 1.28

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 0 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 5 \cdot 10^{+270}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	22.79%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+58}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-12}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 2
Error	15.35%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-27} \lor \neg \left(z \leq 6 \cdot 10^{-60}\right):\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 3
Error	21%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+56}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4
Error	2%
Cost	836

\[\begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 5
Error	22.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 6
Error	21.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 7
Error	2.23%
Cost	704

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

Alternative 8
Error	30.59%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 9
Error	44.52%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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))))