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

Average Error: 16.7 → 5.6

Time: 35.1s

Precision: binary64

Cost: 4560

Math

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

↓

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ t_3 := \left(x + y\right) - \frac{1}{t - a} \cdot \left(y \cdot \left(t - z\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(\frac{y \cdot z}{t} + x\right) - \frac{a \cdot y}{t}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (- (* (/ z (- t a)) y) (- x)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t))))
        (t_3 (- (+ x y) (* (/ 1.0 (- t a)) (* y (- t z))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-241)
       t_3
       (if (<= t_2 0.0)
         (- (+ (/ (* y z) t) x) (/ (* a y) t))
         (if (<= t_2 2e+270) t_3 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 = ((z / (t - a)) * y) - -x;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double t_3 = (x + y) - ((1.0 / (t - a)) * (y * (t - z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (((y * z) / t) + x) - ((a * y) / t);
	} else if (t_2 <= 2e+270) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 = ((z / (t - a)) * y) - -x;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double t_3 = (x + y) - ((1.0 / (t - a)) * (y * (t - z)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-241) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (((y * z) / t) + x) - ((a * y) / t);
	} else if (t_2 <= 2e+270) {
		tmp = t_3;
	} 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 = ((z / (t - a)) * y) - -x
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	t_3 = (x + y) - ((1.0 / (t - a)) * (y * (t - z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-241:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = (((y * z) / t) + x) - ((a * y) / t)
	elif t_2 <= 2e+270:
		tmp = t_3
	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(Float64(z / Float64(t - a)) * y) - Float64(-x))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	t_3 = Float64(Float64(x + y) - Float64(Float64(1.0 / Float64(t - a)) * Float64(y * Float64(t - z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y * z) / t) + x) - Float64(Float64(a * y) / t));
	elseif (t_2 <= 2e+270)
		tmp = t_3;
	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 = ((z / (t - a)) * y) - -x;
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	t_3 = (x + y) - ((1.0 / (t - a)) * (y * (t - z)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-241)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = (((y * z) / t) + x) - ((a * y) / t);
	elseif (t_2 <= 2e+270)
		tmp = t_3;
	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[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * y), $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]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] - N[(N[(1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-241], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+270], t$95$3, t$95$1]]]]]]]

Target

Original	16.7
Target	8.4
Herbie	5.6

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or 2.0000000000000001e270 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 52.3

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

   2. Applied egg-rr 22.6

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

   3. Applied egg-rr 22.6

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

   4. Applied egg-rr 15.7

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

   5. Taylor expanded in t around inf 20.9

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

   6. Simplified 20.9

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.9999999999999999e-241 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 2.0000000000000001e270

   1. Initial program 1.4

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

   2. Applied egg-rr 1.5

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

   if -1.9999999999999999e-241 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 58.8

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

   2. Applied egg-rr 58.7

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

   3. Applied egg-rr 58.7

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

   4. Applied egg-rr 42.2

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

   5. Taylor expanded in t around inf 2.3

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

Alternatives

Alternative 1
Error	5.2
Cost	9352

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ t_2 := \mathsf{fma}\left(\frac{t}{t - a}, y, -\left(x + y\right)\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;\frac{y}{t - a} \cdot z - t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(\frac{y \cdot z}{t} + x\right) - \frac{a \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t - a} \cdot y - t_2\\ \end{array} \]

Alternative 2
Error	5.2
Cost	8452

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;\frac{y}{t - a} \cdot z - \mathsf{fma}\left(\frac{t}{t - a}, y, -\left(x + y\right)\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(\frac{y \cdot z}{t} + x\right) - \frac{a \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t - a} \cdot y + \left(\frac{t}{a - t} \cdot y + \left(x + y\right)\right)\\ \end{array} \]

Alternative 3
Error	5.6
Cost	4432

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{y \cdot \left(z - a\right)}{t} + x\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	5.6
Cost	4432

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(\frac{y \cdot z}{t} + x\right) - \frac{a \cdot y}{t}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	5.2
Cost	3016

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y + \left(\frac{t}{a - t} \cdot y + \left(x + y\right)\right)\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(\frac{y \cdot z}{t} + x\right) - \frac{a \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	9.1
Cost	1360

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{a - t} \cdot \left(z - t\right)\\ t_2 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ \mathbf{if}\;t \leq -7500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+143}:\\ \;\;\;\;\frac{y \cdot \left(z - a\right)}{t} + x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	9.0
Cost	1360

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+122}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+143}:\\ \;\;\;\;\frac{y \cdot \left(z - a\right)}{t} + x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+236}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	9.9
Cost	1096

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ \mathbf{if}\;t \leq -0.195:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+59}:\\ \;\;\;\;\left(x + y\right) - \frac{-1}{t - a} \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	8.8
Cost	968

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+66}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{a - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	9.8
Cost	968

\[\begin{array}{l} t_1 := \frac{z}{t - a} \cdot y - \left(-x\right)\\ \mathbf{if}\;t \leq -27000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	9.4
Cost	904

\[\begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{a} \cdot z\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{z}{t - a} \cdot y - \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{a} \cdot y\\ \end{array} \]

Alternative 12
Error	13.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-71}:\\ \;\;\;\;\frac{y \cdot \left(z - a\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13
Error	11.3
Cost	840

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{a} \cdot z\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{y \cdot \left(z - a\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	11.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-51}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{a} \cdot z\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y \cdot \left(z - a\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{a} \cdot y\\ \end{array} \]

Alternative 15
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-71}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 16
Error	19.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-90}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 17
Error	27.2
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-156}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-81}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	28.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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))))