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

Average Error: 38.62% → 7.62%

Time: 22.2s

Precision: binary64

Cost: 9417

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ t_2 := \frac{y - z}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-274} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(x, 1 - t_2, t \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y}{z} \cdot \left(x - t\right) - \frac{x - t}{\frac{z}{a}}\right)\\ \end{array} \]

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 (+ x (/ (* (- y z) (- t x)) (- a z)))) (t_2 (/ (- y z) (- a z))))
   (if (or (<= t_1 -4e-274) (not (<= t_1 0.0)))
     (fma x (- 1.0 t_2) (* t t_2))
     (+ t (- (* (/ y z) (- x t)) (/ (- x t) (/ z a)))))))

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 = x + (((y - z) * (t - x)) / (a - z));
	double t_2 = (y - z) / (a - z);
	double tmp;
	if ((t_1 <= -4e-274) || !(t_1 <= 0.0)) {
		tmp = fma(x, (1.0 - t_2), (t * t_2));
	} else {
		tmp = t + (((y / z) * (x - t)) - ((x - t) / (z / a)));
	}
	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(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	t_2 = Float64(Float64(y - z) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= -4e-274) || !(t_1 <= 0.0))
		tmp = fma(x, Float64(1.0 - t_2), Float64(t * t_2));
	else
		tmp = Float64(t + Float64(Float64(Float64(y / z) * Float64(x - t)) - Float64(Float64(x - t) / Float64(z / a))));
	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[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-274], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x * N[(1.0 - t$95$2), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] - N[(N[(x - t), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	38.62%
Target	19.33%
Herbie	7.62%

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.99999999999999986e-274 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 33.49

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

   2. Simplified 16.98

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

      [Start] 33.49	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 33.49	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*r/ [<=] 17.02	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]
      *-commutative [<=] 17.02	\[ \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} + x \]
      fma-def [=>] 16.98	\[ \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)} \]

   3. Taylor expanded in x around 0 25.78

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

   4. Simplified 8.03

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

      [Start] 25.78	\[ \left(1 + -1 \cdot \frac{y - z}{a - z}\right) \cdot x + \frac{t \cdot \left(y - z\right)}{a - z} \]
      *-commutative [=>] 25.78	\[ \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} + \frac{t \cdot \left(y - z\right)}{a - z} \]
      fma-def [=>] 25.78	\[ \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \frac{y - z}{a - z}, \frac{t \cdot \left(y - z\right)}{a - z}\right)} \]
      mul-1-neg [=>] 25.78	\[ \mathsf{fma}\left(x, 1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}, \frac{t \cdot \left(y - z\right)}{a - z}\right) \]
      unsub-neg [=>] 25.78	\[ \mathsf{fma}\left(x, \color{blue}{1 - \frac{y - z}{a - z}}, \frac{t \cdot \left(y - z\right)}{a - z}\right) \]
      associate-*r/ [<=] 8.03	\[ \mathsf{fma}\left(x, 1 - \frac{y - z}{a - z}, \color{blue}{t \cdot \frac{y - z}{a - z}}\right) \]

   if -3.99999999999999986e-274 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 92.95

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

   2. Simplified 92.94

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

      [Start] 92.95	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 92.95	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*r/ [<=] 93.17	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]
      *-commutative [<=] 93.17	\[ \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} + x \]
      fma-def [=>] 92.94	\[ \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)} \]

   3. Taylor expanded in z around inf 3.23

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

   4. Simplified 3.34

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

      [Start] 3.23	\[ -1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) \]
      +-commutative [=>] 3.23	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 3.23	\[ \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 3.23	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) - \frac{y \cdot \left(t - x\right)}{z}} \]
      associate--l+ [=>] 3.23	\[ \color{blue}{t + \left(\frac{a \cdot \left(t - x\right)}{z} - \frac{y \cdot \left(t - x\right)}{z}\right)} \]
      *-commutative [=>] 3.23	\[ t + \left(\frac{\color{blue}{\left(t - x\right) \cdot a}}{z} - \frac{y \cdot \left(t - x\right)}{z}\right) \]
      associate-/l* [=>] 3.5	\[ t + \left(\color{blue}{\frac{t - x}{\frac{z}{a}}} - \frac{y \cdot \left(t - x\right)}{z}\right) \]
      associate-/l* [=>] 8.47	\[ t + \left(\frac{t - x}{\frac{z}{a}} - \color{blue}{\frac{y}{\frac{z}{t - x}}}\right) \]
      associate-/r/ [=>] 3.34	\[ t + \left(\frac{t - x}{\frac{z}{a}} - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 7.62

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4 \cdot 10^{-274} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(x, 1 - \frac{y - z}{a - z}, t \cdot \frac{y - z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y}{z} \cdot \left(x - t\right) - \frac{x - t}{\frac{z}{a}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	10.89%
Cost	2889

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-274} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y}{z} \cdot \left(x - t\right) - \frac{x - t}{\frac{z}{a}}\right)\\ \end{array} \]

Alternative 2
Error	10.88%
Cost	2633

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-274} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3
Error	37.84%
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - z \cdot \frac{t}{a - z}\\ t_3 := x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 7500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	30.63%
Cost	1496

\[\begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y}}\\ t_2 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 5
Error	45.57%
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -15000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-57}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 9:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	45.53%
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -68000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 70:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	45.21%
Cost	1108

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -3500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 0.13:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	45.22%
Cost	1108

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -190000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-56}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 0.022:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	39.74%
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	37.53%
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 7200:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	37.92%
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+128}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 25000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12
Error	37.62%
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1.3:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	56.11%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	23.92%
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-58} \lor \neg \left(a \leq 3.8 \cdot 10^{-26}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 15
Error	58.66%
Cost	780

\[\begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	49.38%
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{+128} \lor \neg \left(a \leq 155000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 17
Error	56.39%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	71.37%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023121 
(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))))