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

Average Error: 24.8 → 6.5

Time: 46.1s

Precision: binary64

Cost: 7620

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2241998158227108 \cdot 10^{+192}:\\ \;\;\;\;t + \left(\frac{a}{z} + 1\right) \cdot \frac{t - x}{\frac{z}{\mathsf{fma}\left(-1, y, a\right)}}\\ \mathbf{elif}\;z \leq 9.57747643772307 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(1 + \frac{y - z}{z - a}\right) + t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

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 -1.2241998158227108e+192)
   (+ t (* (+ (/ a z) 1.0) (/ (- t x) (/ z (fma -1.0 y a)))))
   (if (<= z 9.57747643772307e+257)
     (+ (* x (+ 1.0 (/ (- y z) (- z a)))) (* t (/ (- z y) (- z a))))
     (+ t (/ (- x t) (/ z (- y 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 tmp;
	if (z <= -1.2241998158227108e+192) {
		tmp = t + (((a / z) + 1.0) * ((t - x) / (z / fma(-1.0, y, a))));
	} else if (z <= 9.57747643772307e+257) {
		tmp = (x * (1.0 + ((y - z) / (z - a)))) + (t * ((z - y) / (z - a)));
	} else {
		tmp = t + ((x - t) / (z / (y - 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)
	tmp = 0.0
	if (z <= -1.2241998158227108e+192)
		tmp = Float64(t + Float64(Float64(Float64(a / z) + 1.0) * Float64(Float64(t - x) / Float64(z / fma(-1.0, y, a)))));
	elseif (z <= 9.57747643772307e+257)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(Float64(y - z) / Float64(z - a)))) + Float64(t * Float64(Float64(z - y) / Float64(z - a))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - 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_] := If[LessEqual[z, -1.2241998158227108e+192], N[(t + N[(N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z / N[(-1.0 * y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.57747643772307e+257], N[(N[(x * N[(1.0 + N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	24.8
Target	11.8
Herbie	6.5

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

Derivation

1. Split input into 3 regimes

2. if z < -1.2241998158227108e192

   1. Initial program 49.5

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

   2. Taylor expanded in z around inf 29.4

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

   3. Simplified 7.1

      \[\leadsto \color{blue}{t + \left(\frac{a}{z} + 1\right) \cdot \frac{t - x}{\frac{z}{\mathsf{fma}\left(-1, y, a\right)}}} \]
      Proof
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (-.f64 t x) (/.f64 z (fma.f64 -1 y a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (-.f64 t x) (/.f64 z (fma.f64 -1 y (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 a)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (-.f64 t x) (/.f64 z (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 -1 y) (neg.f64 a))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 (*.f64 -1 y) (neg.f64 a))) z)))): 47 points increase in error, 14 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (*.f64 -1 y) (-.f64 t x)) (*.f64 (neg.f64 a) (-.f64 t x)))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (-.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 y (-.f64 t x)))) (*.f64 (neg.f64 a) (-.f64 t x))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (Rewrite=> distribute-lft-neg-out_binary64 (neg.f64 (*.f64 a (-.f64 t x))))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 a (-.f64 t x))))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (+.f64 (/.f64 a z) 1) (/.f64 (Rewrite=> distribute-lft-out--_binary64 (*.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 (+.f64 (/.f64 a z) 1) (Rewrite<= associate-*r/_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<= distribute-lft1-in_binary64 (+.f64 (*.f64 (/.f64 a z) (*.f64 -1 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z))) (*.f64 -1 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z))))): 0 points increase in error, 1 points decrease in error
      (+.f64 t (+.f64 (*.f64 (/.f64 a z) (Rewrite=> mul-1-neg_binary64 (neg.f64 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z)))) (*.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 (+.f64 (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (/.f64 a z) (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z)))) (*.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 (+.f64 (neg.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) (*.f64 z z)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z)))): 24 points increase in error, 3 points decrease in error
      (+.f64 t (+.f64 (neg.f64 (/.f64 (*.f64 a (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) (Rewrite<= unpow2_binary64 (pow.f64 z 2)))) (*.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 (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 a (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) (pow.f64 z 2)))) (*.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
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 t (*.f64 -1 (/.f64 (*.f64 a (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) (pow.f64 z 2)))) (*.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 (+.f64 t (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (*.f64 a (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))))) (pow.f64 z 2)))) (*.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 (+.f64 t (/.f64 (*.f64 -1 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) a))) (pow.f64 z 2))) (*.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 (+.f64 t (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 -1 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) a)) (pow.f64 z 2))) (*.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 (+.f64 t (/.f64 (*.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (*.f64 -1 (*.f64 a (-.f64 t x))))) a) (pow.f64 z 2))) (*.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 (+.f64 t (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 a (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (*.f64 -1 (*.f64 a (-.f64 t x)))))) (pow.f64 z 2))) (*.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 (+.f64 t (/.f64 (*.f64 a (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (*.f64 -1 (*.f64 a (-.f64 t x))))) (pow.f64 z 2))) (*.f64 -1 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 y (-.f64 t x)) z) (/.f64 (*.f64 a (-.f64 t x)) z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 t (/.f64 (*.f64 a (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (*.f64 -1 (*.f64 a (-.f64 t x))))) (pow.f64 z 2))) (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.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
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 t (/.f64 (*.f64 a (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (*.f64 -1 (*.f64 a (-.f64 t x))))) (pow.f64 z 2))) (*.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)) (+.f64 t (/.f64 (*.f64 a (-.f64 (*.f64 -1 (*.f64 y (-.f64 t x))) (*.f64 -1 (*.f64 a (-.f64 t x))))) (pow.f64 z 2))))) (*.f64 -1 (/.f64 (*.f64 a (-.f64 t x)) z))): 0 points increase in error, 0 points decrease in error

   if -1.2241998158227108e192 < z < 9.57747643772306959e257

   1. Initial program 19.9

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

   2. Simplified 11.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{x - t}{z - a}, x\right)} \]
      Proof
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 x t) (-.f64 z a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (-.f64 x t)))) (-.f64 z a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (neg.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 x t)))) (-.f64 z a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (neg.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 x) t))) (-.f64 z a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (neg.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 x)) t)) (-.f64 z a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 t (neg.f64 x)))) (-.f64 z a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 t x))) (-.f64 z a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (neg.f64 (-.f64 t x)) (-.f64 z a)))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (/.f64 (neg.f64 (-.f64 t x)) (-.f64 z a))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (neg.f64 (-.f64 t x))) (*.f64 -1 (-.f64 z a)))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (neg.f64 (-.f64 t x)))) (*.f64 -1 (-.f64 z a))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (Rewrite=> remove-double-neg_binary64 (-.f64 t x)) (*.f64 -1 (-.f64 z a))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 z a)))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 z a)))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 z) a))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 z)) a)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (Rewrite<= +-commutative_binary64 (+.f64 a (neg.f64 z)))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (Rewrite<= sub-neg_binary64 (-.f64 a z))) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x)): 23 points increase in error, 16 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) x): 96 points increase in error, 32 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

   3. Taylor expanded in x around 0 14.4

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

   4. Simplified 6.5

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{y - z}{z - a}\right) - t \cdot \frac{y - z}{z - a}} \]
      Proof
      (-.f64 (*.f64 x (+.f64 1 (/.f64 (-.f64 y z) (-.f64 z a)))) (*.f64 t (/.f64 (-.f64 y z) (-.f64 z a)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 x (+.f64 1 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 y (-.f64 z a)) (/.f64 z (-.f64 z a)))))) (*.f64 t (/.f64 (-.f64 y z) (-.f64 z a)))): 0 points increase in error, 1 points decrease in error
      (-.f64 (*.f64 x (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 1 (/.f64 y (-.f64 z a))) (/.f64 z (-.f64 z a))))) (*.f64 t (/.f64 (-.f64 y z) (-.f64 z a)))): 0 points increase in error, 2 points decrease in error
      (-.f64 (*.f64 x (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 y (-.f64 z a)) 1)) (/.f64 z (-.f64 z a)))) (*.f64 t (/.f64 (-.f64 y z) (-.f64 z a)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (+.f64 (/.f64 y (-.f64 z a)) 1) (/.f64 z (-.f64 z a))) x)) (*.f64 t (/.f64 (-.f64 y z) (-.f64 z a)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (*.f64 (-.f64 (+.f64 (/.f64 y (-.f64 z a)) 1) (/.f64 z (-.f64 z a))) x) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 z a)))): 52 points increase in error, 7 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 (-.f64 (+.f64 (/.f64 y (-.f64 z a)) 1) (/.f64 z (-.f64 z a))) x) (neg.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 z a))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (-.f64 (+.f64 (/.f64 y (-.f64 z a)) 1) (/.f64 z (-.f64 z a))) x) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 z a))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 z a))) (*.f64 (-.f64 (+.f64 (/.f64 y (-.f64 z a)) 1) (/.f64 z (-.f64 z a))) x))): 0 points increase in error, 0 points decrease in error

   if 9.57747643772306959e257 < z

   1. Initial program 54.0

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

   2. Applied egg-rr 34.3

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

   3. Applied egg-rr 34.3

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

   4. Taylor expanded in z around inf 22.0

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

   5. Simplified 6.0

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]
      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))): 53 points increase in error, 27 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, 0 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 (*.f64 -1 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 y (-.f64 t x)) z) (/.f64 (*.f64 a (-.f64 t x)) z))))): 0 points increase in error, 1 points decrease in error
      (+.f64 t (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.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
      (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
3. Recombined 3 regimes into one program.

4. Final simplification 6.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2241998158227108 \cdot 10^{+192}:\\ \;\;\;\;t + \left(\frac{a}{z} + 1\right) \cdot \frac{t - x}{\frac{z}{\mathsf{fma}\left(-1, y, a\right)}}\\ \mathbf{elif}\;z \leq 9.57747643772307 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(1 + \frac{y - z}{z - a}\right) + t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.8
Cost	4560

\[\begin{array}{l} t_1 := x + \frac{1}{\frac{\frac{a - z}{t - x}}{y - z}}\\ t_2 := x - \frac{\left(t - x\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.8
Cost	4432

\[\begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 3
Error	34.9
Cost	2028

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -6.2331861055735385 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.801465503587207 \cdot 10^{-16}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq -6.237375252461967 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.645091239470882 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.628021794871173 \cdot 10^{-140}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;y \leq -1.4210449490287223 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.0786194778717717 \cdot 10^{-267}:\\ \;\;\;\;t - \frac{a \cdot x}{z}\\ \mathbf{elif}\;y \leq 7.938188206855629 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.995236911902822 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;y \leq 12956444409.446606:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{+91}:\\ \;\;\;\;x + \frac{z \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	11.0
Cost	1884

\[\begin{array}{l} t_1 := x + \frac{1}{\frac{\frac{a - z}{t - x}}{y - z}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.361816749560688 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-207}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.778594459751128 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.034049821056684 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.408524764536363 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.57747643772307 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \frac{y}{z} + t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	10.9
Cost	1884

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ t_2 := \frac{a - z}{t - x}\\ t_3 := x + \frac{1}{\frac{t_2}{y - z}}\\ \mathbf{if}\;z \leq -1.361816749560688 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-100}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10^{-275}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.084434490426945 \cdot 10^{+61}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{1}{t_2}\\ \mathbf{elif}\;z \leq 5.034049821056684 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.408524764536363 \cdot 10^{+199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.57747643772307 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \frac{y}{z} + t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	6.6
Cost	1608

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.2241998158227108 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.57747643772307 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(1 + \frac{y - z}{z - a}\right) + t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	18.1
Cost	1496

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.8559725556906693 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3009545643412528 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.304544904237476 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	18.1
Cost	1496

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.8559725556906693 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3009545643412528 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-35}:\\ \;\;\;\;t + \left(a - y\right) \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.304544904237476 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	17.7
Cost	1496

\[\begin{array}{l} t_1 := x + z \cdot \frac{t - x}{z - a}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.361816749560688 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -156833753472428.13:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.778594459751128 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	14.8
Cost	1364

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.306865675195793 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-207}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 46000:\\ \;\;\;\;x + \frac{1}{\frac{a - z}{\left(t - x\right) \cdot y}}\\ \mathbf{elif}\;z \leq 4.778594459751128 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	35.2
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{\frac{z}{z - y}}\\ \mathbf{if}\;a \leq -3.081315860114551 \cdot 10^{+240}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.0927206113092226 \cdot 10^{+172}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.169883785435105 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.718117601367533 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	20.6
Cost	1236

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.8559725556906693 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3009545643412528 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1343287419997524 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.811350671608306 \cdot 10^{+85}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	20.6
Cost	1236

\[\begin{array}{l} t_1 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.8559725556906693 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3009545643412528 \cdot 10^{+60}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1343287419997524 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.811350671608306 \cdot 10^{+85}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	20.2
Cost	1236

\[\begin{array}{l} t_1 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.8559725556906693 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3009545643412528 \cdot 10^{+60}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.304544904237476 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.811350671608306 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	14.1
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.306865675195793 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-207}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.778594459751128 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	25.1
Cost	1104

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5.288013366469641 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -156833753472428.13:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 2.3236429707731397 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \]

Alternative 17
Error	24.6
Cost	1104

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.8559725556906693 \cdot 10^{+90}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a}}\\ \mathbf{elif}\;z \leq -156833753472428.13:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 2.3236429707731397 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \]

Alternative 18
Error	20.5
Cost	1104

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.8559725556906693 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3009545643412528 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3236429707731397 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	34.3
Cost	976

\[\begin{array}{l} t_1 := \frac{t}{\frac{z}{z - y}}\\ \mathbf{if}\;a \leq -2.169883785435105 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.718117601367533 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	32.2
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -3.081315860114551 \cdot 10^{+240}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.0927206113092226 \cdot 10^{+172}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.169883785435105 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.718117601367533 \cdot 10^{+111}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	32.2
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -3.081315860114551 \cdot 10^{+240}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.0927206113092226 \cdot 10^{+172}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.169883785435105 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{z}{\frac{-a}{x}}\\ \mathbf{elif}\;a \leq 6.718117601367533 \cdot 10^{+111}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	32.4
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -3.081315860114551 \cdot 10^{+240}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.134933853663551 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.169883785435105 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{z}{\frac{-a}{x}}\\ \mathbf{elif}\;a \leq 6.718117601367533 \cdot 10^{+111}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Error	36.4
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -2.169883785435105 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-232}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.075806864926343 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	35.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -2.169883785435105 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.075806864926343 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25
Error	46.0
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022300 
(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))))