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

Average Error: 16.83% → 2.08%

Time: 9.0s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-215} \lor \neg \left(z \leq 1.9 \cdot 10^{-265}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e-215) (not (<= z 1.9e-265)))
   (+ x (* (/ (- y z) (- a z)) t))
   (+ x (/ (* (- y z) t) (- a z)))))

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 tmp;
	if ((z <= -8.5e-215) || !(z <= 1.9e-265)) {
		tmp = x + (((y - z) / (a - z)) * t);
	} else {
		tmp = x + (((y - z) * t) / (a - z));
	}
	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) :: tmp
    if ((z <= (-8.5d-215)) .or. (.not. (z <= 1.9d-265))) then
        tmp = x + (((y - z) / (a - z)) * t)
    else
        tmp = x + (((y - z) * t) / (a - z))
    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 tmp;
	if ((z <= -8.5e-215) || !(z <= 1.9e-265)) {
		tmp = x + (((y - z) / (a - z)) * t);
	} else {
		tmp = x + (((y - z) * t) / (a - z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e-215) or not (z <= 1.9e-265):
		tmp = x + (((y - z) / (a - z)) * t)
	else:
		tmp = x + (((y - z) * t) / (a - z))
	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)
	tmp = 0.0
	if ((z <= -8.5e-215) || !(z <= 1.9e-265))
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	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)
	tmp = 0.0;
	if ((z <= -8.5e-215) || ~((z <= 1.9e-265)))
		tmp = x + (((y - z) / (a - z)) * t);
	else
		tmp = x + (((y - z) * t) / (a - z));
	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_] := If[Or[LessEqual[z, -8.5e-215], N[Not[LessEqual[z, 1.9e-265]], $MachinePrecision]], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	16.83%
Target	0.96%
Herbie	2.08%

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

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999998e-215 or 1.8999999999999999e-265 < z

   1. Initial program 18.05

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

   2. Simplified 1.6

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

      [Start] 18.05	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 1.6	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -8.4999999999999998e-215 < z < 1.8999999999999999e-265

   1. Initial program 6.25

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

4. Final simplification 2.08

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-215} \lor \neg \left(z \leq 1.9 \cdot 10^{-265}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	18.35%
Cost	1236

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+129}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+34}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-266}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 2
Error	17.69%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+130} \lor \neg \left(z \leq 2.1 \cdot 10^{+15}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 3
Error	13.63%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+34} \lor \neg \left(z \leq 3.2 \cdot 10^{+45}\right):\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 4
Error	13.66%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+52}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y - z}{z}\\ \end{array} \]

Alternative 5
Error	21.98%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+26} \lor \neg \left(z \leq 2.9 \cdot 10^{+14}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 6
Error	22.09%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+27} \lor \neg \left(z \leq 1050000000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7
Error	22.06%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+26} \lor \neg \left(z \leq 2.9 \cdot 10^{+14}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8
Error	2.02%
Cost	704

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

Alternative 9
Error	30.66%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 480000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 10
Error	44.63%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023089 
(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))))