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

Average Error: 16.53% → 1.92%

Time: 10.5s

Precision: binary64

Cost: 968

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.7e+46)
   (+ x (* (/ y (- z a)) (- z t)))
   (if (<= y 5e-217)
     (+ x (/ (* y (- z t)) (- z a)))
     (+ x (/ y (/ (- z a) (- z t)))))))

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 tmp;
	if (y <= -2.7e+46) {
		tmp = x + ((y / (z - a)) * (z - t));
	} else if (y <= 5e-217) {
		tmp = x + ((y * (z - t)) / (z - a));
	} else {
		tmp = x + (y / ((z - a) / (z - t)));
	}
	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) :: tmp
    if (y <= (-2.7d+46)) then
        tmp = x + ((y / (z - a)) * (z - t))
    else if (y <= 5d-217) then
        tmp = x + ((y * (z - t)) / (z - a))
    else
        tmp = x + (y / ((z - a) / (z - t)))
    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 tmp;
	if (y <= -2.7e+46) {
		tmp = x + ((y / (z - a)) * (z - t));
	} else if (y <= 5e-217) {
		tmp = x + ((y * (z - t)) / (z - a));
	} else {
		tmp = x + (y / ((z - a) / (z - t)));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.7e+46:
		tmp = x + ((y / (z - a)) * (z - t))
	elif y <= 5e-217:
		tmp = x + ((y * (z - t)) / (z - a))
	else:
		tmp = x + (y / ((z - a) / (z - t)))
	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)
	tmp = 0.0
	if (y <= -2.7e+46)
		tmp = Float64(x + Float64(Float64(y / Float64(z - a)) * Float64(z - t)));
	elseif (y <= 5e-217)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	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)
	tmp = 0.0;
	if (y <= -2.7e+46)
		tmp = x + ((y / (z - a)) * (z - t));
	elseif (y <= 5e-217)
		tmp = x + ((y * (z - t)) / (z - a));
	else
		tmp = x + (y / ((z - a) / (z - t)));
	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_] := If[LessEqual[y, -2.7e+46], N[(x + N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-217], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	16.53%
Target	1.82%
Herbie	1.92%

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

Derivation

1. Split input into 3 regimes

2. if y < -2.7000000000000002e46

   1. Initial program 42.6

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

   2. Simplified 4.9

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

      [Start] 42.6	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-*l/ [<=] 4.9	\[ x + \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

   if -2.7000000000000002e46 < y < 5.0000000000000002e-217

   1. Initial program 1.09

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

   if 5.0000000000000002e-217 < y

   1. Initial program 19.18

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

   2. Simplified 1.34

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

      [Start] 19.18	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-/l* [=>] 1.34	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.92

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]

Alternatives

Alternative 1
Error	22.09%
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{+247}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 2
Error	37.2%
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-123}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-5}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+202}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	21.82%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+247}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 10^{+200}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4
Error	22.98%
Cost	908

\[\begin{array}{l} \mathbf{if}\;z \leq -1050000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Error	4.3%
Cost	836

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+201}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array} \]

Alternative 6
Error	21.82%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -42000 \lor \neg \left(z \leq 1.06 \cdot 10^{+17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 7
Error	21.87%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -0.4:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+18}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	21.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	1.82%
Cost	704

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

Alternative 10
Error	30.04%
Cost	457

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-54} \lor \neg \left(z \leq 10^{+17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	44%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(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))))