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

Average Error: 38.56% → 10.76%

Time: 24.7s

Precision: binary64

Cost: 8004

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-287}:\\ \;\;\;\;\mathsf{fma}\left(t_1, t - x, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot t_1\\ \end{array} \]

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 -2e-287)
     (fma t_1 (- t x) x)
     (if (<= t_2 0.0) (+ t (* (- t x) (/ (- a y) z))) (+ 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 <= -2e-287) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = t + ((t - x) * ((a - y) / z));
	} 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 <= -2e-287)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	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, -2e-287], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	38.56%
Target	18.99%
Herbie	10.76%

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000004e-287

   1. Initial program 32.55

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

   2. Simplified 11.19

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

      [Start] 32.55	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 32.55	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*l/ [<=] 11.21	\[ \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]
      fma-def [=>] 11.19	\[ \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   if -2.00000000000000004e-287 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 93.74

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

   2. Simplified 93.73

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

      [Start] 93.74	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 93.74	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*l/ [<=] 93.73	\[ \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]
      fma-def [=>] 93.73	\[ \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Taylor expanded in z around inf 2.04

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

   4. Simplified 2.42

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

      [Start] 2.04	\[ \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 2.04	\[ \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]
      distribute-lft-out-- [=>] 2.04	\[ t + \frac{\color{blue}{\left(-1 \cdot \left(y - a\right)\right)} \cdot \left(t - x\right)}{z} \]
      associate-*r* [<=] 2.04	\[ t + \frac{\color{blue}{-1 \cdot \left(\left(y - a\right) \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r/ [<=] 2.04	\[ t + \color{blue}{-1 \cdot \frac{\left(y - a\right) \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 2.04	\[ t + \color{blue}{\left(-\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 2.04	\[ \color{blue}{t - \frac{\left(y - a\right) \cdot \left(t - x\right)}{z}} \]
      associate-/l* [=>] 10.51	\[ t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]
      associate-/r/ [=>] 2.42	\[ t - \color{blue}{\frac{y - a}{z} \cdot \left(t - x\right)} \]

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

   1. Initial program 33.91

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

   2. Simplified 11.94

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

      [Start] 33.91	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 11.94	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 10.76

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z} \leq -2 \cdot 10^{-287}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z} \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.77%
Cost	2633

\[\begin{array}{l} t_1 := x + \frac{\left(x - t\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-287} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]

Alternative 2
Error	44.79%
Cost	1765

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.11 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-189}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-209}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-47} \lor \neg \left(t \leq 8.2 \cdot 10^{+142}\right) \land t \leq 1.8 \cdot 10^{+166}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	53.37%
Cost	1504

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-36}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-126}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+103}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	60.33%
Cost	1372

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z - a}\\ t_2 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+116}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+67}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	37.52%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 6
Error	37.6%
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -3.35 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+97}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00022:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 7
Error	37.6%
Cost	1368

\[\begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+97}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-7}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+54}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 8
Error	49.88%
Cost	1304

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -950000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-282}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \end{array} \]

Alternative 9
Error	49.79%
Cost	1240

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	52.54%
Cost	1108

\[\begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+155}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Error	35.34%
Cost	1106

\[\begin{array}{l} \mathbf{if}\;z \leq -55000000000 \lor \neg \left(z \leq -5.8 \cdot 10^{-23}\right) \land \left(z \leq -1.1 \cdot 10^{-90} \lor \neg \left(z \leq 3.05 \cdot 10^{-40}\right)\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 12
Error	26.88%
Cost	1100

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-64}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-37}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	49.26%
Cost	978

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+15} \lor \neg \left(z \leq -4.4 \cdot 10^{-23}\right) \land \left(z \leq -1.1 \cdot 10^{-90} \lor \neg \left(z \leq 3.6 \cdot 10^{-11}\right)\right):\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 14
Error	43.95%
Cost	977

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+251} \lor \neg \left(x \leq 1.08 \cdot 10^{+276}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15
Error	57.06%
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+155}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Error	55.91%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Error	55.97%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	55.46%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	71.08%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023090 
(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))))