Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Error: 2.1 → 1.4

Time: 8.2s

Precision: binary64

Cost: 7240

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{1}{t} \cdot \left(y - x\right), x\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{+41}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma z (* (/ 1.0 t) (- y x)) x)))
   (if (<= z -1e+100) t_1 (if (<= z 1e+41) (+ x (/ (- y x) (/ t z))) t_1))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = fma(z, ((1.0 / t) * (y - x)), x);
	double tmp;
	if (z <= -1e+100) {
		tmp = t_1;
	} else if (z <= 1e+41) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t)
	t_1 = fma(z, Float64(Float64(1.0 / t) * Float64(y - x)), x)
	tmp = 0.0
	if (z <= -1e+100)
		tmp = t_1;
	elseif (z <= 1e+41)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(1.0 / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1e+100], t$95$1, If[LessEqual[z, 1e+41], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	2.1
Target	2.3
Herbie	1.4

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000002e100 or 1.00000000000000001e41 < z

   1. Initial program 5.0

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

   2. Applied egg-rr 2.2

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

   if -1.00000000000000002e100 < z < 1.00000000000000001e41

   1. Initial program 1.0

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

   2. Applied egg-rr 1.1

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

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{1}{t} \cdot \left(y - x\right), x\right)\\ \mathbf{elif}\;z \leq 10^{+41}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{1}{t} \cdot \left(y - x\right), x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	21.6
Cost	1424

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	21.4
Cost	1424

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{elif}\;\frac{z}{t} \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \end{array} \]

Alternative 3
Error	21.4
Cost	1424

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{elif}\;\frac{z}{t} \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 4
Error	12.1
Cost	1228

\[\begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	4.4
Cost	1228

\[\begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -10000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	5.0
Cost	1228

\[\begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -10000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	1.4
Cost	1220

\[\begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq -5 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 8
Error	0.7
Cost	1096

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+241}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]

Alternative 9
Error	13.6
Cost	968

\[\begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	21.3
Cost	840

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	21.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 12
Error	21.6
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 13
Error	17.7
Cost	712

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-219}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	30.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022329 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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