Linear.V4:$cdot from linear-1.19.1.3, C

Average Error: 0.0 → 22.2

Time: 12.0s

Precision: binary64

Cost: 8540

Math

\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

↓

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + y \cdot x\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(y, x, a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-197}:\\ \;\;\;\;a \cdot b + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-293}:\\ \;\;\;\;y \cdot x + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, a \cdot b\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

↓

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y x) (* a b))))
   (if (<= (* c i) -5e+19)
     (+ (* c i) (* y x))
     (if (<= (* c i) -2e-160)
       (fma y x (* a b))
       (if (<= (* c i) -1e-197)
         (+ (* a b) (* t z))
         (if (<= (* c i) -1e-275)
           t_1
           (if (<= (* c i) 5e-293)
             (+ (* y x) (* t z))
             (if (<= (* c i) 4e-188)
               t_1
               (if (<= (* c i) 2e+35)
                 (fma y x (* t z))
                 (fma c i (* a b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * x) + (a * b);
	double tmp;
	if ((c * i) <= -5e+19) {
		tmp = (c * i) + (y * x);
	} else if ((c * i) <= -2e-160) {
		tmp = fma(y, x, (a * b));
	} else if ((c * i) <= -1e-197) {
		tmp = (a * b) + (t * z);
	} else if ((c * i) <= -1e-275) {
		tmp = t_1;
	} else if ((c * i) <= 5e-293) {
		tmp = (y * x) + (t * z);
	} else if ((c * i) <= 4e-188) {
		tmp = t_1;
	} else if ((c * i) <= 2e+35) {
		tmp = fma(y, x, (t * z));
	} else {
		tmp = fma(c, i, (a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

↓

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * x) + Float64(a * b))
	tmp = 0.0
	if (Float64(c * i) <= -5e+19)
		tmp = Float64(Float64(c * i) + Float64(y * x));
	elseif (Float64(c * i) <= -2e-160)
		tmp = fma(y, x, Float64(a * b));
	elseif (Float64(c * i) <= -1e-197)
		tmp = Float64(Float64(a * b) + Float64(t * z));
	elseif (Float64(c * i) <= -1e-275)
		tmp = t_1;
	elseif (Float64(c * i) <= 5e-293)
		tmp = Float64(Float64(y * x) + Float64(t * z));
	elseif (Float64(c * i) <= 4e-188)
		tmp = t_1;
	elseif (Float64(c * i) <= 2e+35)
		tmp = fma(y, x, Float64(t * z));
	else
		tmp = fma(c, i, Float64(a * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5e+19], N[(N[(c * i), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2e-160], N[(y * x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1e-197], N[(N[(a * b), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1e-275], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 5e-293], N[(N[(y * x), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4e-188], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2e+35], N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision], N[(c * i + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if (*.f64 c i) < -5e19

   1. Initial program 0.0

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Taylor expanded in x around inf 21.1

      \[\leadsto \color{blue}{y \cdot x} + c \cdot i \]

   if -5e19 < (*.f64 c i) < -2e-160

   1. Initial program 0.0

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Simplified 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\right)} \]

   3. Taylor expanded in z around 0 18.5

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c \cdot i + a \cdot b}\right) \]

   4. Taylor expanded in c around 0 24.0

      \[\leadsto \color{blue}{a \cdot b + y \cdot x} \]

   5. Simplified 24.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, a \cdot b\right)} \]

   if -2e-160 < (*.f64 c i) < -9.9999999999999999e-198

   1. Initial program 0.0

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Simplified 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\right)} \]

   3. Taylor expanded in c around 0 1.5

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

   4. Simplified 1.5

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

   5. Taylor expanded in y around 0 20.1

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if -9.9999999999999999e-198 < (*.f64 c i) < -9.99999999999999934e-276 or 5.0000000000000003e-293 < (*.f64 c i) < 3.9999999999999998e-188

   1. Initial program 0.0

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Simplified 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\right)} \]

   3. Taylor expanded in z around 0 21.5

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c \cdot i + a \cdot b}\right) \]

   4. Taylor expanded in c around 0 22.3

      \[\leadsto \color{blue}{a \cdot b + y \cdot x} \]

   if -9.99999999999999934e-276 < (*.f64 c i) < 5.0000000000000003e-293

   1. Initial program 0.0

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Simplified 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\right)} \]

   3. Taylor expanded in a around 0 22.4

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c \cdot i + t \cdot z}\right) \]

   4. Taylor expanded in c around 0 22.4

      \[\leadsto \color{blue}{y \cdot x + t \cdot z} \]

   if 3.9999999999999998e-188 < (*.f64 c i) < 1.9999999999999999e35

   1. Initial program 0.0

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Simplified 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\right)} \]

   3. Taylor expanded in a around 0 18.0

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c \cdot i + t \cdot z}\right) \]

   4. Taylor expanded in c around 0 26.5

      \[\leadsto \color{blue}{y \cdot x + t \cdot z} \]

   5. Simplified 26.4

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

   if 1.9999999999999999e35 < (*.f64 c i)

   1. Initial program 0.0

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]

   2. Applied egg-rr 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)} \]

   3. Taylor expanded in a around inf 17.5

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{a \cdot b}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 22.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + y \cdot x\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(y, x, a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-197}:\\ \;\;\;\;a \cdot b + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-275}:\\ \;\;\;\;y \cdot x + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-293}:\\ \;\;\;\;y \cdot x + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-188}:\\ \;\;\;\;y \cdot x + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, a \cdot b\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	22.2
Cost	8540

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + y \cdot x\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(y, x, a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-197}:\\ \;\;\;\;a \cdot b + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-293}:\\ \;\;\;\;y \cdot x + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 2
Error	22.2
Cost	7240

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ t_2 := y \cdot x + t \cdot z\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + y \cdot x\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(y, x, a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-197}:\\ \;\;\;\;a \cdot b + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 3
Error	37.7
Cost	2792

\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.0921649536798919 \cdot 10^{+49}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.38969163587648 \cdot 10^{-13}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \cdot i \leq -3.065814026272141 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -4.325821343461614 \cdot 10^{-130}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \cdot i \leq -9.995103455371166 \cdot 10^{-209}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.6936764813 \cdot 10^{-314}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \cdot i \leq 2.4337197697230637 \cdot 10^{-210}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5.2137743837314386 \cdot 10^{-176}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \cdot i \leq 6.3571648393653564 \cdot 10^{-74}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 1.5579540771888221 \cdot 10^{+35}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 4
Error	22.2
Cost	2268

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ t_2 := y \cdot x + t \cdot z\\ \mathbf{if}\;c \cdot i \leq -5.946016544694227 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + y \cdot x\\ \mathbf{elif}\;c \cdot i \leq -3.2952542024009906 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -1.8023883484232276 \cdot 10^{-197}:\\ \;\;\;\;a \cdot b + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq -1.1598427972431649 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 3.046023912528629 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2.2062193131170184 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.5579540771888221 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 5
Error	22.1
Cost	1748

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ t_2 := y \cdot x + t \cdot z\\ \mathbf{if}\;c \cdot i \leq -1.0005989168943282 \cdot 10^{+77}:\\ \;\;\;\;c \cdot i + t \cdot z\\ \mathbf{elif}\;c \cdot i \leq -1.1598427972431649 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 3.046023912528629 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2.2062193131170184 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.5579540771888221 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 6
Error	22.3
Cost	1748

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ t_2 := y \cdot x + t \cdot z\\ \mathbf{if}\;c \cdot i \leq -5.946016544694227 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + y \cdot x\\ \mathbf{elif}\;c \cdot i \leq -1.1598427972431649 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 3.046023912528629 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2.2062193131170184 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.5579540771888221 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 7
Error	42.6
Cost	1644

\[\begin{array}{l} \mathbf{if}\;c \leq -2.568984570490513 \cdot 10^{+80}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq -2.0528060063256314 \cdot 10^{+23}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq -2.0572944628234372 \cdot 10^{-19}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq -1.3217045131797286 \cdot 10^{-123}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq -1.7498912317196447 \cdot 10^{-137}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \leq -4.661421606941242 \cdot 10^{-183}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq -2.321250122550184 \cdot 10^{-248}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \leq 2.2634391848109535 \cdot 10^{-265}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 5.421280622468299 \cdot 10^{-190}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \leq 9.899099823779427 \cdot 10^{-159}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 2.4681573428920208 \cdot 10^{-119}:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 8
Error	27.2
Cost	1504

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ t_2 := c \cdot i + a \cdot b\\ t_3 := c \cdot i + t \cdot z\\ \mathbf{if}\;c \leq -2.568984570490513 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.4815227351111136 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.0572944628234372 \cdot 10^{-19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.3217045131797286 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.7498912317196447 \cdot 10^{-137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.661421606941242 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.817380221729894 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.6416078631815134 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	25.8
Cost	1488

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -1.0005989168943282 \cdot 10^{+77}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 5.710622157848145 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 6.3571648393653564 \cdot 10^{-74}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 1.5579540771888221 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 10
Error	22.7
Cost	1488

\[\begin{array}{l} t_1 := y \cdot x + a \cdot b\\ t_2 := c \cdot i + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -4.9669456410843076 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 5.710622157848145 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 6.3571648393653564 \cdot 10^{-74}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 1.5579540771888221 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	37.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.0921649536798919 \cdot 10^{+49}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 63624657773256.56:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 12
Error	47.5
Cost	192

\[t \cdot z \]

Reproduce

herbie shell --seed 2022228 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))