Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Average Error: 7.4 → 0.9

Time: 17.4s

Precision: binary64

Cost: 6096

Math

\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

↓

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t_1}{z}}}{x + 1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) - \frac{x}{\left(z \cdot t\right) \cdot \left(x + 1\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -1e+14)
     (/ (+ x (/ y (/ t_1 z))) (+ x 1.0))
     (if (<= t_2 2e-48)
       (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
       (if (<= t_2 2e+26)
         t_2
         (if (<= t_2 INFINITY)
           (* y (/ (/ z (+ x 1.0)) t_1))
           (-
            (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0))))
            (/ x (* (* z t) (+ x 1.0))))))))))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

↓

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	} else if (t_2 <= 2e-48) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_2 <= 2e+26) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else {
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / ((z * t) * (x + 1.0)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+14) {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	} else if (t_2 <= 2e-48) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_2 <= 2e+26) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else {
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / ((z * t) * (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

↓

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e+14:
		tmp = (x + (y / (t_1 / z))) / (x + 1.0)
	elif t_2 <= 2e-48:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	elif t_2 <= 2e+26:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = y * ((z / (x + 1.0)) / t_1)
	else:
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / ((z * t) * (x + 1.0)))
	return tmp

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+14)
		tmp = Float64(Float64(x + Float64(y / Float64(t_1 / z))) / Float64(x + 1.0));
	elseif (t_2 <= 2e-48)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	elseif (t_2 <= 2e+26)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(y * Float64(Float64(z / Float64(x + 1.0)) / t_1));
	else
		tmp = Float64(Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0)))) - Float64(x / Float64(Float64(z * t) * Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+14)
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	elseif (t_2 <= 2e-48)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	elseif (t_2 <= 2e+26)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = y * ((z / (x + 1.0)) / t_1);
	else
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / ((z * t) * (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+14], N[(N[(x + N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-48], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+26], t$95$2, If[LessEqual[t$95$2, Infinity], N[(y * N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(z * t), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	7.4
Target	0.4
Herbie	0.9

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

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -1e14

   1. Initial program 16.6

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

   2. Simplified 16.6

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
      Proof
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 t z)) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in y around inf 16.6

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

   4. Simplified 1.3

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t \cdot z - x}{z}}}}{x + 1} \]
      Proof
      (/.f64 (+.f64 x (/.f64 y (/.f64 (-.f64 (*.f64 t z) x) z))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 x (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y z) (-.f64 (*.f64 t z) x)))) (+.f64 x 1)): 0 points increase in error, 2 points decrease in error

   if -1e14 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.9999999999999999e-48

   1. Initial program 3.2

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

   2. Simplified 3.2

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
      Proof
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 t z)) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in t around -inf 1.1

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

   if 1.9999999999999999e-48 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2.0000000000000001e26

   1. Initial program 0.0

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

   if 2.0000000000000001e26 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < +inf.0

   1. Initial program 19.6

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

   2. Simplified 19.6

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
      Proof
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 t z)) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in y around inf 19.6

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

   4. Simplified 7.1

      \[\leadsto \color{blue}{\frac{y}{\frac{\left(x + 1\right) \cdot \left(t \cdot z - x\right)}{z}}} \]
      Proof
      (/.f64 (+.f64 x (/.f64 y (/.f64 (-.f64 (*.f64 t z) x) z))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 x (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y z) (-.f64 (*.f64 t z) x)))) (+.f64 x 1)): 0 points increase in error, 2 points decrease in error

   5. Applied egg-rr 4.8

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 64.0

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

   2. Simplified 64.0

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
      Proof
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 t z)) x))) (+.f64 x 1)): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in t around inf 0.0

      \[\leadsto \color{blue}{\left(\frac{x}{1 + x} + \frac{y}{\left(1 + x\right) \cdot t}\right) - \frac{x}{\left(1 + x\right) \cdot \left(t \cdot z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{z \cdot t - x}{z}}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) - \frac{x}{\left(z \cdot t\right) \cdot \left(x + 1\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.9
Cost	5456

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t_1}{z}}}{x + 1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2
Error	3.0
Cost	3144

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq 2 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3
Error	17.5
Cost	1628

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x - \frac{x}{t_1}}{x + 1}\\ t_3 := \frac{y}{t + x \cdot \left(t + \frac{-1}{z}\right)}\\ \mathbf{if}\;x \leq -9 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t_1}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-247}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-285}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]

Alternative 4
Error	12.3
Cost	1556

\[\begin{array}{l} t_1 := \frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{-x}}{x + 1}\\ \mathbf{if}\;z \leq -6 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	7.6
Cost	1225

\[\begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-53} \lor \neg \left(y \leq 2.3 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t_1}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{t_1}}{x + 1}\\ \end{array} \]

Alternative 6
Error	15.9
Cost	1101

\[\begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-43} \lor \neg \left(x \leq 2.9 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 7
Error	15.8
Cost	1100

\[\begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-45}:\\ \;\;\;\;\frac{x - \frac{y \cdot z}{x}}{x + 1}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]

Alternative 8
Error	16.3
Cost	1100

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-28}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]

Alternative 9
Error	22.9
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{\frac{x \cdot \left(-1 - x\right)}{z}}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-179}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-247}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10
Error	17.4
Cost	972

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{\frac{x \cdot \left(-1 - x\right)}{z}}\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-79}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11
Error	17.5
Cost	972

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-49}:\\ \;\;\;\;\frac{-y \cdot z}{x \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12
Error	21.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-225}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13
Error	20.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Error	27.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-189}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15
Error	28.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022340 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))