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

Average Error: 25.0 → 8.0

Time: 48.7s

Precision: binary64

Cost: 7368

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;y + \left(\frac{a}{t} + 1\right) \cdot t_1\\ \mathbf{elif}\;t \leq 1.4868972793242426 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \]

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) (/ t (- z a)))))
   (if (<= t -9.339382262389653e+126)
     (+ y (* (+ (/ a t) 1.0) t_1))
     (if (<= t 1.4868972793242426e+152)
       (fma (- y x) (/ (- z t) (- a t)) x)
       (+ y t_1)))))

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) / (t / (z - a));
	double tmp;
	if (t <= -9.339382262389653e+126) {
		tmp = y + (((a / t) + 1.0) * t_1);
	} else if (t <= 1.4868972793242426e+152) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + t_1;
	}
	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(Float64(x - y) / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (t <= -9.339382262389653e+126)
		tmp = Float64(y + Float64(Float64(Float64(a / t) + 1.0) * t_1));
	elseif (t <= 1.4868972793242426e+152)
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + t_1);
	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[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.339382262389653e+126], N[(y + N[(N[(N[(a / t), $MachinePrecision] + 1.0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4868972793242426e+152], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]]

Target

Original	25.0
Target	10.0
Herbie	8.0

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

Derivation

1. Split input into 3 regimes

2. if t < -9.3393822623896529e126

   1. Initial program 46.2

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

   2. Applied egg-rr 46.2

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

   3. Taylor expanded in t around inf 28.5

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \left(\frac{\left(-1 \cdot \left(\left(y - x\right) \cdot z\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right) \cdot a}{{t}^{2}} + y\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

   4. Simplified 9.7

      \[\leadsto \color{blue}{y - \left(\frac{a}{t} + 1\right) \cdot \frac{y - x}{\frac{t}{z - a}}} \]
      Proof
      (-.f64 y (*.f64 (+.f64 (/.f64 a t) 1) (/.f64 (-.f64 y x) (/.f64 t (-.f64 z a))))): 0 points increase in error, 0 points decrease in error
      (-.f64 y (*.f64 (+.f64 (/.f64 a t) 1) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 y x) (-.f64 z a)) t)))): 37 points increase in error, 11 points decrease in error
      (-.f64 y (*.f64 (+.f64 (/.f64 a t) 1) (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) t))): 0 points increase in error, 0 points decrease in error
      (-.f64 y (*.f64 (+.f64 (/.f64 a t) 1) (/.f64 (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y x) z)) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (-.f64 y (Rewrite<= distribute-lft1-in_binary64 (+.f64 (*.f64 (/.f64 a t) (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t)) (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t)))): 0 points increase in error, 3 points decrease in error
      (-.f64 y (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x)))) (*.f64 t t))) (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 30 points increase in error, 3 points decrease in error
      (-.f64 y (+.f64 (/.f64 (*.f64 a (-.f64 (Rewrite=> *-commutative_binary64 (*.f64 z (-.f64 y x))) (*.f64 a (-.f64 y x)))) (*.f64 t t)) (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (-.f64 y (+.f64 (/.f64 (*.f64 a (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) (Rewrite<= unpow2_binary64 (pow.f64 t 2))) (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 y (neg.f64 (+.f64 (/.f64 (*.f64 a (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) (pow.f64 t 2)) (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (+.f64 (/.f64 (*.f64 a (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) (pow.f64 t 2)) (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 a (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) (pow.f64 t 2))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 y (*.f64 -1 (/.f64 (*.f64 a (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) (pow.f64 t 2)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 y (Rewrite=> mul-1-neg_binary64 (neg.f64 (/.f64 (*.f64 a (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) (pow.f64 t 2))))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> unsub-neg_binary64 (-.f64 y (/.f64 (*.f64 a (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) (pow.f64 t 2)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 y (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x))) a)) (pow.f64 t 2))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 y (/.f64 (*.f64 (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y x) z)) (*.f64 a (-.f64 y x))) a) (pow.f64 t 2))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 y (/.f64 (*.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) a) (Rewrite=> unpow2_binary64 (*.f64 t t)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 y (Rewrite=> times-frac_binary64 (*.f64 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t) (/.f64 a t)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 3 points increase in error, 30 points decrease in error
      (+.f64 (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 y (*.f64 (neg.f64 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t)) (/.f64 a t)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 y (*.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))) (/.f64 a t))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 y (*.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x)))) t)) (/.f64 a t))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 y (*.f64 (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x))))) t) (/.f64 a t))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 y (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (*.f64 t t)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 30 points increase in error, 3 points decrease in error
      (+.f64 (+.f64 y (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (Rewrite<= unpow2_binary64 (pow.f64 t 2)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (pow.f64 t 2)) y)) (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (pow.f64 t 2)) y) (*.f64 -1 (/.f64 (-.f64 (Rewrite=> *-commutative_binary64 (*.f64 z (-.f64 y x))) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (pow.f64 t 2)) y) (*.f64 -1 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 z (-.f64 y x)) t) (/.f64 (*.f64 a (-.f64 y x)) t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (pow.f64 t 2)) y) (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t)) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (pow.f64 t 2)) y) (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t))) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t)) (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x)))) a) (pow.f64 t 2)) y))) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t))): 0 points increase in error, 0 points decrease in error

   if -9.3393822623896529e126 < t < 1.4868972793242426e152

   1. Initial program 15.0

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

   2. Simplified 7.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
      Proof
      (fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))) x)): 3 points increase in error, 4 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) x): 96 points increase in error, 16 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))): 0 points increase in error, 0 points decrease in error

   if 1.4868972793242426e152 < t

   1. Initial program 47.6

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

   2. Applied egg-rr 47.7

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

   3. Taylor expanded in t around inf 23.5

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

   4. Simplified 9.1

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
      Proof
      (-.f64 y (/.f64 (-.f64 y x) (/.f64 t (-.f64 z a)))): 0 points increase in error, 0 points decrease in error
      (-.f64 y (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 y x) (-.f64 z a)) t))): 45 points increase in error, 24 points decrease in error
      (-.f64 y (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x)))) t)): 0 points increase in error, 0 points decrease in error
      (-.f64 y (/.f64 (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y x) z)) (*.f64 a (-.f64 y x))) t)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 y (neg.f64 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t)))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 (-.f64 y x) z) (*.f64 a (-.f64 y x))) t)))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 -1 (/.f64 (-.f64 (Rewrite=> *-commutative_binary64 (*.f64 z (-.f64 y x))) (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 -1 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 z (-.f64 y x)) t) (/.f64 (*.f64 a (-.f64 y x)) t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t)) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 y (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t))) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t)) y)) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 8.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;y + \left(\frac{a}{t} + 1\right) \cdot \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 1.4868972793242426 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	9.6
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-244}:\\ \;\;\;\;y - \left(y - x\right) \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2
Error	42.0
Cost	1904

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ t_2 := \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.847431122890272 \cdot 10^{-26}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -4.879257391494725 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.876843374968846 \cdot 10^{-99}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -8.29325370790701 \cdot 10^{-291}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 9.304084855174914 \cdot 10^{-191}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.4230593794847577 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.201626709249788 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+113}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+269}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 3
Error	18.0
Cost	1628

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 52:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1186191966810364 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{t - a}{x}}\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	20.0
Cost	1500

\[\begin{array}{l} t_1 := y + \frac{x}{t} \cdot \left(z - a\right)\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 52:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.1186191966810364 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{t - a}{x}}\\ \mathbf{elif}\;t \leq 1.0498344928867857 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	16.4
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{a - t}{y - x}}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 52:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	16.4
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{a - t}{y - x}}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y - \left(y - x\right) \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 52:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	15.1
Cost	1492

\[\begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y - \left(y - x\right) \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.708491371972573 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{1}{a - t} \cdot \left(y \cdot \left(z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	21.1
Cost	1368

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{a}{t} + -1}\\ t_2 := y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-20}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 4.017743863221392 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	33.7
Cost	1240

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.868955283775518 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.074607664389046 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.2643134373852116 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.289460309783783 \cdot 10^{+34}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.496421021804267 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;a \leq 2.9820158205488736 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	24.0
Cost	1236

\[\begin{array}{l} t_1 := y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 0.00037:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.19467667709 \cdot 10^{+264}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]

Alternative 11
Error	21.8
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{a}{t} + -1}\\ t_2 := y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-20}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-164}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	19.0
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{a}{t} + -1}\\ t_2 := y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	19.8
Cost	1236

\[\begin{array}{l} t_1 := y + \frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;t \leq -9.339382262389653 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.312314713078289 \cdot 10^{+70}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.0498344928867857 \cdot 10^{+139}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	37.0
Cost	1112

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 52:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.640068565828396 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.922271059707169 \cdot 10^{+117}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.295833114492473 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15
Error	23.0
Cost	1104

\[\begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ t_2 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.5574119891808276 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.074607664389046 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9250404000185013 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	31.4
Cost	1040

\[\begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -2.1346088345048007 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 52:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 4.98436633480356 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a - t}\\ \end{array} \]

Alternative 17
Error	34.8
Cost	976

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.640068565828396 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.0909219350858683 \cdot 10^{+105}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.295833114492473 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18
Error	34.6
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.640068565828396 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.0909219350858683 \cdot 10^{+105}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.295833114492473 \cdot 10^{+156}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 19
Error	30.0
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1346088345048007 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.4368294343394716 \cdot 10^{+49}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.0909219350858683 \cdot 10^{+105}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.0331465404654201 \cdot 10^{+144}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20
Error	30.6
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1346088345048007 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-74}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 0.00037:\\ \;\;\;\;\frac{-t \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 2.640068565828396 \cdot 10^{+53}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21
Error	30.9
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1346088345048007 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 0.00037:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 2.640068565828396 \cdot 10^{+53}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22
Error	36.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 52:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.640068565828396 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23
Error	45.5
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022317 
(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))))