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

Average Error: 16.6 → 5.4

Time: 1.8min

Precision: binary64

Cost: 2632

Math

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

↓

\[\begin{array}{l} t_1 := y \cdot \left(1 + \frac{z - t}{t - a}\right) + x\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y \cdot \frac{z - a}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* y (+ 1.0 (/ (- z t) (- t a)))) x))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -2e-205) t_1 (if (<= t_2 0.0) (+ (* y (/ (- z a) t)) x) t_1))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (1.0 + ((z - t) / (t - a)))) + x;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -2e-205) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = (y * ((z - a) / t)) + x;
	} 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) * y) / (a - t))
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 = (y * (1.0d0 + ((z - t) / (t - a)))) + x
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-2d-205)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = (y * ((z - a) / t)) + x
    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) * y) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (1.0 + ((z - t) / (t - a)))) + x;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -2e-205) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = (y * ((z - a) / t)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = (y * (1.0 + ((z - t) / (t - a)))) + x
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -2e-205:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = (y * ((z - a) / t)) + x
	else:
		tmp = t_1
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a)))) + x)
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-205)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(y * Float64(Float64(z - a) / t)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (1.0 + ((z - t) / (t - a)))) + x;
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-205)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = (y * ((z - a) / t)) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-205], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Target

Original	16.6
Target	8.8
Herbie	5.4

\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-205 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 13.0

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

   2. Applied egg-rr 7.8

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

   3. Applied egg-rr 5.4

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

   if -2e-205 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 54.6

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

   2. Applied egg-rr 54.4

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

   3. Applied egg-rr 32.4

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

   4. Taylor expanded in t around inf 4.4

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

   5. Simplified 4.4

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

Alternatives

Alternative 1
Error	11.4
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z - a}{t} + x\\ t_2 := \left(x + y\right) - \frac{z}{a} \cdot y\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	11.3
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z - a}{t} + x\\ t_2 := \left(x + y\right) - \frac{z}{a} \cdot y\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-28}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{a} \cdot z\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	9.2
Cost	968

\[\begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{z - a}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	13.9
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+108}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{z - a}{t} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Error	15.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+107}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Error	20.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-129}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7
Error	26.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-148}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	29.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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