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

Average Error: 24.4 → 12.2

Time: 21.3s

Precision: binary64

Cost: 2884

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8535004913060756 \cdot 10^{+161}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.324653541786749 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 2.286288309415843 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \mathbf{elif}\;z \leq 1.6315876484854672 \cdot 10^{+199}:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{t \cdot y}{z} + \frac{x \cdot a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8535004913060756e+161)
   (- (+ t (/ (* x y) z)) (/ (* t y) z))
   (if (<= z -2.324653541786749e-205)
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (if (<= z 2.286288309415843e+95)
       (+ x (/ 1.0 (/ (/ (- a z) (- y z)) (- t x))))
       (if (<= z 1.6315876484854672e+199)
         (-
          (+ t (+ (/ (* x y) z) (/ (* t a) z)))
          (+ (/ (* t y) z) (/ (* x a) z)))
         (* t (/ (- y z) (- a z))))))))

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 tmp;
	if (z <= -1.8535004913060756e+161) {
		tmp = (t + ((x * y) / z)) - ((t * y) / z);
	} else if (z <= -2.324653541786749e-205) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (z <= 2.286288309415843e+95) {
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)));
	} else if (z <= 1.6315876484854672e+199) {
		tmp = (t + (((x * y) / z) + ((t * a) / z))) - (((t * y) / z) + ((x * a) / z));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	24.4
Target	11.2
Herbie	12.2

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

Alternatives

Alternative 1
Error	12.6
Cost	2123

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8439181559886184 \cdot 10^{+161}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -4.977241748483381 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 2.665632744970878 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \mathbf{elif}\;z \leq 6.516871611489244 \cdot 10^{+198} \lor \neg \left(z \leq 7.114437549549705 \cdot 10^{+245}\right):\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 2
Error	13.5
Cost	1802

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6970714302335817 \cdot 10^{+161}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 2.665632744970878 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 3.4841224413990884 \cdot 10^{+197} \lor \neg \left(z \leq 9.867617813279591 \cdot 10^{+244}\right):\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 3
Error	18.8
Cost	3086

\[\begin{array}{l} \mathbf{if}\;z \leq -2.6306298374273777 \cdot 10^{+161}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -887261921.2373245:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -5.670244790612329 \cdot 10^{-128}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -2.7635045106747327 \cdot 10^{-155}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 4.02089479195351 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 7.483478574983536 \cdot 10^{+124}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.182944361836499 \cdot 10^{+197} \lor \neg \left(z \leq 1.2534799858847957 \cdot 10^{+246}\right):\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 4
Error	17.8
Cost	2630

\[\begin{array}{l} \mathbf{if}\;z \leq -7.692663948267492 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -956822701.744356:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -5.670244790612329 \cdot 10^{-128}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -2.7635045106747327 \cdot 10^{-155}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 4.106311939096057 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 8.596169924186653 \cdot 10^{+125}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 5
Error	17.9
Cost	2630

\[\begin{array}{l} \mathbf{if}\;z \leq -9.025715939275249 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -887261921.2373245:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -5.670244790612329 \cdot 10^{-128}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -2.7635045106747327 \cdot 10^{-155}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.7240938667409679 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.658347310982765 \cdot 10^{+125}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 6
Error	19.8
Cost	2309

\[\begin{array}{l} \mathbf{if}\;z \leq -2.0721780508316365 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -5.670244790612329 \cdot 10^{-128}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -2.7635045106747327 \cdot 10^{-155}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 6.149420474379798 \cdot 10^{-77}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 0.0065866945820251595:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 7
Error	20.6
Cost	2630

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3103270259764527 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -887261921.2373245:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq -1.7246714973761974 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -6.005786013815118 \cdot 10^{-232}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.5569532409039078 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 0.0065866945820251595:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 8
Error	21.8
Cost	1988

\[\begin{array}{l} \mathbf{if}\;z \leq -8.529374590453773 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -5.670244790612329 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -5.169460605288525 \cdot 10^{-142}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.2817071385661166 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 9
Error	22.5
Cost	1860

\[\begin{array}{l} \mathbf{if}\;z \leq -8.742298527540422 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.85262236547082 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -2.7635045106747327 \cdot 10^{-155}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.091303379474358 \cdot 10^{-59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 10
Error	24.3
Cost	2502

\[\begin{array}{l} \mathbf{if}\;z \leq -7.365371504816024 \cdot 10^{-09}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -7.339211394938965 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq -1.913910439736939 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -5.748322382131514 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.3845003300139345 \cdot 10^{-158}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 8.262591012115391 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 11
Error	24.4
Cost	2502

\[\begin{array}{l} \mathbf{if}\;z \leq -1072757335.9227421:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.7109564584785593 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -2.4985305553648255 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -8.951263263873645 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.3845003300139345 \cdot 10^{-158}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 9.845518832300168 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 12
Error	30.2
Cost	3786

\[\begin{array}{l} \mathbf{if}\;z \leq -1628259091.9017372:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9.16219642062281 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -2.7908406131787685 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -7.34979282300258 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.243803497788972 \cdot 10^{-156}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq -1.614553657580409 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.208541613374156 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2413595796090112 \cdot 10^{-240}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 3.1001407694633076 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.169502092907277 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 13
Error	30.1
Cost	3144

\[\begin{array}{l} \mathbf{if}\;z \leq -980009628.5800333:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -3.0563529010783484 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.5640856989427042 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -7.670086911176793 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.707166683883687 \cdot 10^{-149}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9.466225729732193 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.1198518246928559 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1047612989165766 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Alternative 14
Error	27.9
Cost	1218

\[\begin{array}{l} \mathbf{if}\;a \leq -3.4286492735181634 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.34338611504592 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Alternative 15
Error	35.8
Cost	706

\[\begin{array}{l} \mathbf{if}\;a \leq -4.79594611305097 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.226699184590158 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Alternative 16
Error	45.9
Cost	64

\[x\]

Alternative 17
Error	61.8
Cost	64

\[-1\]

Alternative 18
Error	61.8
Cost	64

\[1\]

Derivation

1. Split input into 5 regimes

2. if z < -1.8535004913060756e161

   1. Initial program 47.8

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

   2. Taylor expanded around 0 24.2

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

   3. Simplified 24.2

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

   4. Simplified 24.2

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

   if -1.8535004913060756e161 < z < -2.32465354178674918e-205

   1. Initial program 17.6

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
   2. Using strategy rm

   3. Applied associate-/l*_binary64_12299 9.7

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

   4. Simplified 9.7

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

   if -2.32465354178674918e-205 < z < 2.28628830941584304e95

   1. Initial program 11.3

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
   2. Using strategy rm

   3. Applied add-cube-cbrt_binary64_12389 11.8

      \[\leadsto x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]

   4. Applied associate-/r*_binary64_12298 11.8

      \[\leadsto x + \color{blue}{\frac{\frac{\left(y - z\right) \cdot \left(t - x\right)}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}{\sqrt[3]{a - z}}}\]

   5. Simplified 6.9

      \[\leadsto x + \frac{\color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(t - x\right)}}{\sqrt[3]{a - z}}\]
   6. Using strategy rm

   7. Applied clear-num_binary64_12353 6.9

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\sqrt[3]{a - z}}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(t - x\right)}}}\]

   8. Simplified 5.4

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}}\]

   9. Simplified 5.4

      \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}}\]

   if 2.28628830941584304e95 < z < 1.63158764848546716e199

   1. Initial program 37.7

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

   2. Taylor expanded around inf 23.7

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

   3. Simplified 23.7

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

   4. Simplified 23.7

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

   if 1.63158764848546716e199 < z

   1. Initial program 50.9

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

   2. Taylor expanded around inf 19.3

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

   3. Simplified 19.3

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}}\]

   4. Simplified 19.3

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}}\]
3. Recombined 5 regimes into one program.

4. Final simplification 12.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8535004913060756 \cdot 10^{+161}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.324653541786749 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 2.286288309415843 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \mathbf{elif}\;z \leq 1.6315876484854672 \cdot 10^{+199}:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{t \cdot y}{z} + \frac{x \cdot a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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))))