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

Average Error: 24.8 → 7.0

Time: 26.9s

Precision: binary64

Cost: 8004

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(t_1, t - x, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))) (t_2 (+ x (/ (* (- x t) (- z y)) (- a z)))))
   (if (<= t_2 -4e-279)
     (fma t_1 (- t x) x)
     (if (<= t_2 0.0) (+ t (/ (- x t) (/ z (- y a)))) (+ x (* (- t x) t_1))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double t_2 = x + (((x - t) * (z - y)) / (a - z));
	double tmp;
	if (t_2 <= -4e-279) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * t_1);
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(Float64(x - t) * Float64(z - y)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -4e-279)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * t_1));
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(x - t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-279], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	24.8
Target	12.0
Herbie	7.0

\[\begin{array}{l} \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.00000000000000022e-279

   1. Initial program 21.7

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

   2. Simplified 7.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
      Proof
      (fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)) x)): 2 points increase in error, 3 points decrease in error
      (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) x): 86 points increase in error, 9 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))): 0 points increase in error, 0 points decrease in error

   if -4.00000000000000022e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 58.4

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

   2. Simplified 58.1

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
      Proof
      (+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))): 86 points increase in error, 9 points decrease in error

   3. Taylor expanded in z around inf 3.1

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

   4. Simplified 3.1

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]
      Proof
      (-.f64 t (/.f64 (-.f64 t x) (/.f64 z (-.f64 y a)))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y a)) z))): 49 points increase in error, 25 points decrease in error
      (-.f64 t (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) z)): 0 points increase in error, 2 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 t (neg.f64 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (*.f64 -1 (*.f64 a (-.f64 t x))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) z) (/.f64 (*.f64 -1 (*.f64 a (-.f64 t x))) z)))): 1 points increase in error, 0 points decrease in error
      (+.f64 t (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (*.f64 y (-.f64 t x)) z))) (/.f64 (*.f64 -1 (*.f64 a (-.f64 t x))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (-.f64 (*.f64 -1 (/.f64 (*.f64 y (-.f64 t x)) z)) (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (*.f64 a (-.f64 t x)) z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 t (*.f64 -1 (/.f64 (*.f64 y (-.f64 t x)) z))) (*.f64 -1 (/.f64 (*.f64 a (-.f64 t x)) z)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 y (-.f64 t x)) z)) t)) (*.f64 -1 (/.f64 (*.f64 a (-.f64 t x)) z))): 0 points increase in error, 0 points decrease in error

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

   1. Initial program 21.5

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

   2. Simplified 7.3

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
      Proof
      (+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))): 86 points increase in error, 9 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 7.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z} \leq -4 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	7.0
Cost	2632

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	28.9
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := \frac{-y}{\frac{a - z}{x}}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -70000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	28.1
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -440000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.3 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	27.9
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7400000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-61}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	15.7
Cost	1496

\[\begin{array}{l} t_1 := x - \frac{z - y}{\frac{a - z}{t}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-284}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{-1}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	16.1
Cost	1364

\[\begin{array}{l} t_1 := x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1150000000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-43}:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	15.8
Cost	1232

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -27500000:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	21.8
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+95}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;z \leq -5800000000000:\\ \;\;\;\;\frac{-t}{\frac{z - a}{y - z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+52}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9
Error	16.4
Cost	1100

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-216}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+46}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	16.4
Cost	1100

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-216}:\\ \;\;\;\;x - \frac{z - y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	24.4
Cost	972

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	30.7
Cost	908

\[\begin{array}{l} t_1 := \frac{t}{\frac{a - z}{-z}}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	32.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+114}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14
Error	32.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15
Error	20.8
Cost	840

\[\begin{array}{l} t_1 := t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -6000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	20.1
Cost	840

\[\begin{array}{l} t_1 := t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -6000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	35.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	35.7
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	35.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Error	32.4
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Error	35.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22
Error	62.1
Cost	64

\[0 \]

Alternative 23
Error	45.6
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022330 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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