Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Average Accuracy: 67.7% → 90.5%

Time: 41.6s

Precision: binary64

Cost: 8004

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-282}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -2e-282)
     (fma (/ (- z t) (- a t)) (- y x) x)
     (if (<= t_1 0.0)
       (+ y (/ (* x (- z a)) t))
       (+ x (/ (- y x) (/ (- a t) (- z t))))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-282) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else if (t_1 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-282)
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-282], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	67.7%
Target	86.3%
Herbie	90.5%

\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-282

   1. Initial program 74.9%

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

   2. Simplified 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
      Step-by-step derivation

      [Start] 74.9	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 74.9	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 93.7	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 93.7	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 93.7	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   if -2e-282 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

   2. Simplified 3.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
      Step-by-step derivation

      [Start] 3.8	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 3.8	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 3.8	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 3.8	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 3.8	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Taylor expanded in t around inf 99.7%

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

   4. Simplified 96.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
      Step-by-step derivation

      [Start] 99.7	\[ y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t} \]
      distribute-lft-out-- [=>] 99.7	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(z - a\right)\right)} \cdot \left(y - x\right)}{t} \]
      associate-*r* [<=] 99.7	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(z - a\right) \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 99.7	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r/ [<=] 99.7	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      mul-1-neg [=>] 99.7	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]
      unsub-neg [=>] 99.7	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      associate-/l* [=>] 96.3	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   5. Taylor expanded in y around 0 99.7%

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

   6. Simplified 99.7%

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

      [Start] 99.7	\[ y - -1 \cdot \frac{\left(z - a\right) \cdot x}{t} \]
      associate-*r/ [=>] 99.7	\[ y - \color{blue}{\frac{-1 \cdot \left(\left(z - a\right) \cdot x\right)}{t}} \]
      *-commutative [=>] 99.7	\[ y - \frac{-1 \cdot \color{blue}{\left(x \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r* [=>] 99.7	\[ y - \frac{\color{blue}{\left(-1 \cdot x\right) \cdot \left(z - a\right)}}{t} \]
      neg-mul-1 [<=] 99.7	\[ y - \frac{\color{blue}{\left(-x\right)} \cdot \left(z - a\right)}{t} \]

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

   1. Initial program 71.4%

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

   2. Simplified 87.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]
      Step-by-step derivation

      [Start] 71.4	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 87.9	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-282}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	90.5%
Cost	2633

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-282} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 2
Accuracy	56.5%
Cost	1500

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+148}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a}{\frac{t}{x}}\\ \end{array} \]

Alternative 3
Accuracy	51.2%
Cost	1372

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - \frac{x}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-141}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-41}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	51.2%
Cost	1372

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - \frac{x}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -1.52 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-142}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-42}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	51.9%
Cost	1372

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - \frac{x}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	51.8%
Cost	1372

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - \frac{a}{\frac{t}{x}}\\ \mathbf{if}\;t \leq -7.1 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	55.4%
Cost	1368

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - \frac{a}{\frac{t}{x}}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-42}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+149}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	55.2%
Cost	1368

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - \frac{a}{\frac{t}{x}}\\ t_3 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-141}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-82}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+160}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	36.6%
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-163}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10
Accuracy	35.3%
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-149}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 11
Accuracy	51.4%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y - \frac{a}{\frac{t}{x}}\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-141}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+149}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	65.2%
Cost	1232

\[\begin{array}{l} t_1 := y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{x - y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-74}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	72.1%
Cost	1232

\[\begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{x - y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-74}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	52.2%
Cost	1108

\[\begin{array}{l} t_1 := y - \frac{x}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	65.2%
Cost	1105

\[\begin{array}{l} t_1 := y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-76} \lor \neg \left(t \leq 6.5 \cdot 10^{-32}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 16
Accuracy	65.6%
Cost	1105

\[\begin{array}{l} t_1 := y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{x - y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-76} \lor \neg \left(t \leq 7.6 \cdot 10^{-32}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 17
Accuracy	84.0%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+75} \lor \neg \left(t \leq 9.2 \cdot 10^{+75}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

Alternative 18
Accuracy	36.9%
Cost	980

\[\begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 19
Accuracy	36.9%
Cost	980

\[\begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-149}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20
Accuracy	48.5%
Cost	976

\[\begin{array}{l} t_1 := y + y \cdot \frac{a}{t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Accuracy	65.0%
Cost	972

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-69}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+152}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a}{\frac{t}{x}}\\ \end{array} \]

Alternative 22
Accuracy	65.1%
Cost	972

\[\begin{array}{l} t_1 := y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-74}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a}{\frac{t}{x}}\\ \end{array} \]

Alternative 23
Accuracy	48.4%
Cost	848

\[\begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+85}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 24
Accuracy	66.5%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+74} \lor \neg \left(t \leq 8 \cdot 10^{-32}\right):\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 25
Accuracy	47.4%
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 26
Accuracy	37.2%
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 13500:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 27
Accuracy	37.2%
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.86 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.009:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 28
Accuracy	38.9%
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 29
Accuracy	25.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023159 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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