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

Average Accuracy: 96.8% → 96.8%

Time: 12.1s

Precision: binary64

Cost: 7112

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq 6.2 \cdot 10^{-279}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= x 6.2e-279)
   (+ x (/ (- y x) (/ t z)))
   (if (<= x 2e-76)
     (+ x (/ 1.0 (/ t (* (- y x) z))))
     (fma (- y x) (/ z t) x))))

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 tmp;
	if (x <= 6.2e-279) {
		tmp = x + ((y - x) / (t / z));
	} else if (x <= 2e-76) {
		tmp = x + (1.0 / (t / ((y - x) * z)));
	} else {
		tmp = fma((y - x), (z / t), x);
	}
	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)
	tmp = 0.0
	if (x <= 6.2e-279)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	elseif (x <= 2e-76)
		tmp = Float64(x + Float64(1.0 / Float64(t / Float64(Float64(y - x) * z))));
	else
		tmp = fma(Float64(y - x), Float64(z / t), x);
	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_] := If[LessEqual[x, 6.2e-279], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-76], N[(x + N[(1.0 / N[(t / N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]]

Target

Original	96.8%
Target	96.6%
Herbie	96.8%

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

Derivation

1. Split input into 3 regimes

2. if x < 6.1999999999999998e-279

   1. Initial program 96.5%

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

   2. Applied egg-rr 96.6%

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

      [Start] 96.5	\[ x + \left(y - x\right) \cdot \frac{z}{t} \]
      clear-num [=>] 96.3	\[ x + \left(y - x\right) \cdot \color{blue}{\frac{1}{\frac{t}{z}}} \]
      un-div-inv [=>] 96.6	\[ x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   if 6.1999999999999998e-279 < x < 1.99999999999999985e-76

   1. Initial program 93.3%

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

   2. Applied egg-rr 92.6%

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

      [Start] 93.3	\[ x + \left(y - x\right) \cdot \frac{z}{t} \]
      associate-*r/ [=>] 92.7	\[ x + \color{blue}{\frac{\left(y - x\right) \cdot z}{t}} \]
      clear-num [=>] 92.6	\[ x + \color{blue}{\frac{1}{\frac{t}{\left(y - x\right) \cdot z}}} \]

   if 1.99999999999999985e-76 < x

   1. Initial program 99.5%

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

   2. Simplified 99.5%

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

      [Start] 99.5	\[ x + \left(y - x\right) \cdot \frac{z}{t} \]
      +-commutative [=>] 99.5	\[ \color{blue}{\left(y - x\right) \cdot \frac{z}{t} + x} \]
      fma-def [=>] 99.5	\[ \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.2 \cdot 10^{-279}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	81.1%
Cost	1229

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -20000000000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 2
Accuracy	96.4%
Cost	1229

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -10000 \lor \neg \left(\frac{z}{t} \leq 0.02\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 3
Accuracy	96.5%
Cost	1228

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.02:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 4
Accuracy	65.0%
Cost	1164

\[\begin{array}{l} t_1 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	64.7%
Cost	1164

\[\begin{array}{l} t_1 := \left(-z\right) \cdot \frac{x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	64.8%
Cost	1164

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 7
Accuracy	77.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-23} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	76.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+42} \lor \neg \left(\frac{z}{t} \leq 5000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 9
Accuracy	96.8%
Cost	968

\[\begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{-279}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10
Accuracy	57.5%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-163} \lor \neg \left(x \leq -4.7 \cdot 10^{-228}\right) \land x \leq 1.8 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	65.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-23} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	65.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-23} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	64.4%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-23}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 14
Accuracy	97.9%
Cost	836

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+278}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 15
Accuracy	97.9%
Cost	836

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1.3 \cdot 10^{+280}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 16
Accuracy	50.2%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(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))))