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

Average Accuracy: 61.5% → 87.4%

Time: 24.8s

Precision: binary64

Cost: 7236

Math

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

↓

\[\begin{array}{l} t_1 := \frac{z}{y - a}\\ t_2 := \frac{x - t}{t_1}\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t - x}{t_1}, t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+141}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{a}{z} \cdot t_2\right) + t_2\\ \end{array} \]

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 (/ z (- y a))) (t_2 (/ (- x t) t_1)))
   (if (<= z -8.4e+116)
     (fma -1.0 (/ (- t x) t_1) t)
     (if (<= z 2.3e+141)
       (+ x (* (- t x) (/ (- y z) (- a z))))
       (+ (+ t (* (/ a z) t_2)) t_2)))))

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 = z / (y - a);
	double t_2 = (x - t) / t_1;
	double tmp;
	if (z <= -8.4e+116) {
		tmp = fma(-1.0, ((t - x) / t_1), t);
	} else if (z <= 2.3e+141) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = (t + ((a / z) * t_2)) + t_2;
	}
	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(z / Float64(y - a))
	t_2 = Float64(Float64(x - t) / t_1)
	tmp = 0.0
	if (z <= -8.4e+116)
		tmp = fma(-1.0, Float64(Float64(t - x) / t_1), t);
	elseif (z <= 2.3e+141)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(Float64(t + Float64(Float64(a / z) * t_2)) + t_2);
	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[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - t), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[z, -8.4e+116], N[(-1.0 * N[(N[(t - x), $MachinePrecision] / t$95$1), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 2.3e+141], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(N[(a / z), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Target

Original	61.5%
Target	81.5%
Herbie	87.4%

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

Derivation

1. Split input into 3 regimes

2. if z < -8.4000000000000005e116

   1. Initial program 30.7%

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

   2. Simplified 66.9%

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

      [Start] 30.7	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 66.9	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Taylor expanded in z around -inf 64.3%

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

   4. Simplified 83.9%

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

      [Start] 64.3	\[ -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} + t \]
      fma-def [=>] 64.3	\[ \color{blue}{\mathsf{fma}\left(-1, \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}, t\right)} \]
      distribute-rgt-out-- [=>] 64.3	\[ \mathsf{fma}\left(-1, \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}, t\right) \]
      associate-/l* [=>] 83.9	\[ \mathsf{fma}\left(-1, \color{blue}{\frac{t - x}{\frac{z}{y - a}}}, t\right) \]

   if -8.4000000000000005e116 < z < 2.3000000000000002e141

   1. Initial program 77.7%

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

   2. Simplified 89.0%

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

      [Start] 77.7	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 89.0	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   if 2.3000000000000002e141 < z

   1. Initial program 27.3%

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

   2. Simplified 65.7%

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

      [Start] 27.3	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 65.7	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Applied egg-rr 27.3%

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

   4. Taylor expanded in z around inf 53.2%

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

   5. Simplified 84.5%

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

      [Start] 53.2	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 53.2	\[ \color{blue}{\left(\left(t + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 53.2	\[ \color{blue}{\left(t + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t - x}{\frac{z}{y - a}}, t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+141}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{a}{z} \cdot \frac{x - t}{\frac{z}{y - a}}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.6%
Cost	2633

\[\begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-234} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]

Alternative 2
Accuracy	87.4%
Cost	1864

\[\begin{array}{l} t_1 := \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+116}:\\ \;\;\;\;t + \left(\frac{t - x}{\frac{z}{a}} + \frac{y}{z} \cdot \left(x - t\right)\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+137}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{a}{z} \cdot t_1\right) + t_1\\ \end{array} \]

Alternative 3
Accuracy	44.7%
Cost	1832

\[\begin{array}{l} t_1 := x + \frac{t \cdot y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+268}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-275}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \frac{-t}{a - z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1100000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 4
Accuracy	51.3%
Cost	1764

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_3 := x + \frac{t \cdot y}{a}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-274}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-304}:\\ \;\;\;\;z \cdot \frac{-t}{a - z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-153}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2100000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	72.7%
Cost	1364

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+218}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]

Alternative 6
Accuracy	73.2%
Cost	1364

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-83}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+220}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]

Alternative 7
Accuracy	87.5%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+116} \lor \neg \left(z \leq 3.6 \cdot 10^{+146}\right):\\ \;\;\;\;t + \left(\frac{t - x}{\frac{z}{a}} + \frac{y}{z} \cdot \left(x - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 8
Accuracy	87.5%
Cost	1352

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+116}:\\ \;\;\;\;t + \left(\frac{t - x}{\frac{z}{a}} + t_1\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+146}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(t - x\right) \cdot \frac{a}{z}\right) + t_1\\ \end{array} \]

Alternative 9
Accuracy	53.6%
Cost	1240

\[\begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.07 \cdot 10^{+127}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	72.9%
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]

Alternative 11
Accuracy	65.6%
Cost	1104

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -0.0018:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]

Alternative 12
Accuracy	53.6%
Cost	976

\[\begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 13
Accuracy	66.6%
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+200}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]

Alternative 14
Accuracy	66.5%
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+200}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]

Alternative 15
Accuracy	49.7%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+87}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Accuracy	45.2%
Cost	460

\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+157}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-57}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Accuracy	44.0%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	29.3%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023141 
(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))))