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

Percentage Accurate: 89.2% → 97.2%

Time: 13.2s

Precision: binary64

Cost: 3784

Math

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

↓

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z \cdot \frac{1}{\frac{t_1}{y}} + \left(x - -1\right)}{x + 1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{\left(z \cdot t\right) \cdot \left(x + 1\right)}\\ \end{array} \]

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 (- INFINITY))
     (/ (+ (* z (/ 1.0 (/ t_1 y))) (- x -1.0)) (+ x 1.0))
     (if (<= t_2 5e+263)
       t_2
       (-
        (+ (/ y (* t (+ x 1.0))) (/ x (+ 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 <= -((double) INFINITY)) {
		tmp = ((z * (1.0 / (t_1 / y))) + (x - -1.0)) / (x + 1.0);
	} else if (t_2 <= 5e+263) {
		tmp = t_2;
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (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 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z * (1.0 / (t_1 / y))) + (x - -1.0)) / (x + 1.0);
	} else if (t_2 <= 5e+263) {
		tmp = t_2;
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (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 <= -math.inf:
		tmp = ((z * (1.0 / (t_1 / y))) + (x - -1.0)) / (x + 1.0)
	elif t_2 <= 5e+263:
		tmp = t_2
	else:
		tmp = ((y / (t * (x + 1.0))) + (x / (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 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z * Float64(1.0 / Float64(t_1 / y))) + Float64(x - -1.0)) / Float64(x + 1.0));
	elseif (t_2 <= 5e+263)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / Float64(t * Float64(x + 1.0))) + Float64(x / 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 <= -Inf)
		tmp = ((z * (1.0 / (t_1 / y))) + (x - -1.0)) / (x + 1.0);
	elseif (t_2 <= 5e+263)
		tmp = t_2;
	else
		tmp = ((y / (t * (x + 1.0))) + (x / (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, (-Infinity)], N[(N[(N[(z * N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - -1.0), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+263], t$95$2, N[(N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(z * t), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	89.2%
Target	99.5%
Herbie	97.2%

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 30.0%

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

   2. Simplified 30.0%

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

      [Start] 30.0%	\[ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
      *-commutative [=>] 30.0%	\[ \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Applied egg-rr 93.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{z}{1}, \frac{y}{z \cdot t - x}, -\left(\frac{x}{z \cdot t - x} - x\right)\right)}}{x + 1} \]
      Step-by-step derivation

      [Start] 30.0%	\[ \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \]
      +-commutative [=>] 30.0%	\[ \frac{\color{blue}{\frac{y \cdot z - x}{z \cdot t - x} + x}}{x + 1} \]
      div-sub [=>] 30.0%	\[ \frac{\color{blue}{\left(\frac{y \cdot z}{z \cdot t - x} - \frac{x}{z \cdot t - x}\right)} + x}{x + 1} \]
      associate-+l- [=>] 30.0%	\[ \frac{\color{blue}{\frac{y \cdot z}{z \cdot t - x} - \left(\frac{x}{z \cdot t - x} - x\right)}}{x + 1} \]
      *-commutative [=>] 30.0%	\[ \frac{\frac{\color{blue}{z \cdot y}}{z \cdot t - x} - \left(\frac{x}{z \cdot t - x} - x\right)}{x + 1} \]
      *-un-lft-identity [=>] 30.0%	\[ \frac{\frac{z \cdot y}{\color{blue}{1 \cdot \left(z \cdot t - x\right)}} - \left(\frac{x}{z \cdot t - x} - x\right)}{x + 1} \]
      times-frac [=>] 93.5%	\[ \frac{\color{blue}{\frac{z}{1} \cdot \frac{y}{z \cdot t - x}} - \left(\frac{x}{z \cdot t - x} - x\right)}{x + 1} \]
      fma-neg [=>] 93.5%	\[ \frac{\color{blue}{\mathsf{fma}\left(\frac{z}{1}, \frac{y}{z \cdot t - x}, -\left(\frac{x}{z \cdot t - x} - x\right)\right)}}{x + 1} \]

   4. Simplified 93.5%

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

      [Start] 93.5%	\[ \frac{\mathsf{fma}\left(\frac{z}{1}, \frac{y}{z \cdot t - x}, -\left(\frac{x}{z \cdot t - x} - x\right)\right)}{x + 1} \]
      fma-udef [=>] 93.5%	\[ \frac{\color{blue}{\frac{z}{1} \cdot \frac{y}{z \cdot t - x} + \left(-\left(\frac{x}{z \cdot t - x} - x\right)\right)}}{x + 1} \]
      unsub-neg [=>] 93.5%	\[ \frac{\color{blue}{\frac{z}{1} \cdot \frac{y}{z \cdot t - x} - \left(\frac{x}{z \cdot t - x} - x\right)}}{x + 1} \]
      /-rgt-identity [=>] 93.5%	\[ \frac{\color{blue}{z} \cdot \frac{y}{z \cdot t - x} - \left(\frac{x}{z \cdot t - x} - x\right)}{x + 1} \]
      *-commutative [=>] 93.5%	\[ \frac{z \cdot \frac{y}{\color{blue}{t \cdot z} - x} - \left(\frac{x}{z \cdot t - x} - x\right)}{x + 1} \]
      *-commutative [=>] 93.5%	\[ \frac{z \cdot \frac{y}{t \cdot z - x} - \left(\frac{x}{\color{blue}{t \cdot z} - x} - x\right)}{x + 1} \]

   5. Applied egg-rr 93.6%

      \[\leadsto \frac{z \cdot \color{blue}{{\left(\frac{\mathsf{fma}\left(z, t, -x\right)}{y}\right)}^{-1}} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]
      Step-by-step derivation

      [Start] 93.5%	\[ \frac{z \cdot \frac{y}{t \cdot z - x} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]
      clear-num [=>] 93.6%	\[ \frac{z \cdot \color{blue}{\frac{1}{\frac{t \cdot z - x}{y}}} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]
      inv-pow [=>] 93.6%	\[ \frac{z \cdot \color{blue}{{\left(\frac{t \cdot z - x}{y}\right)}^{-1}} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]
      *-commutative [=>] 93.6%	\[ \frac{z \cdot {\left(\frac{\color{blue}{z \cdot t} - x}{y}\right)}^{-1} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]
      fma-neg [=>] 93.6%	\[ \frac{z \cdot {\left(\frac{\color{blue}{\mathsf{fma}\left(z, t, -x\right)}}{y}\right)}^{-1} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]

   6. Simplified 93.6%

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

      [Start] 93.6%	\[ \frac{z \cdot {\left(\frac{\mathsf{fma}\left(z, t, -x\right)}{y}\right)}^{-1} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]
      unpow-1 [=>] 93.6%	\[ \frac{z \cdot \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(z, t, -x\right)}{y}}} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]
      fma-neg [<=] 93.6%	\[ \frac{z \cdot \frac{1}{\frac{\color{blue}{z \cdot t - x}}{y}} - \left(\frac{x}{t \cdot z - x} - x\right)}{x + 1} \]

   7. Taylor expanded in x around inf 93.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5.00000000000000022e263

   1. Initial program 99.3%

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

   if 5.00000000000000022e263 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 17.9%

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

   2. Simplified 17.9%

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

      [Start] 17.9%	\[ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
      *-commutative [=>] 17.9%	\[ \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Taylor expanded in t around inf 87.9%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{z \cdot \frac{1}{\frac{z \cdot t - x}{y}} + \left(x - -1\right)}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{\left(z \cdot t\right) \cdot \left(x + 1\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.2%
Cost	3784

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z \cdot \frac{1}{\frac{t_1}{y}} + \left(x - -1\right)}{x + 1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{\left(z \cdot t\right) \cdot \left(x + 1\right)}\\ \end{array} \]

Alternative 2
Accuracy	96.5%
Cost	3400

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t_1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + 1} \cdot \left(x + \frac{y}{t}\right)\\ \end{array} \]

Alternative 3
Accuracy	97.2%
Cost	3400

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z \cdot \frac{y}{t_1} + \left(x - -1\right)}{x + 1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + 1} \cdot \left(x + \frac{y}{t}\right)\\ \end{array} \]

Alternative 4
Accuracy	97.2%
Cost	3400

\[\begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z \cdot \frac{1}{\frac{t_1}{y}} + \left(x - -1\right)}{x + 1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + 1} \cdot \left(x + \frac{y}{t}\right)\\ \end{array} \]

Alternative 5
Accuracy	86.2%
Cost	1488

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{z \cdot t - x}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-254}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	67.8%
Cost	1236

\[\begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-14}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \frac{y}{x \cdot x}\\ \end{array} \]

Alternative 7
Accuracy	83.4%
Cost	1234

\[\begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-15} \lor \neg \left(t \leq -1.2 \cdot 10^{-81}\right) \land \left(t \leq -1.3 \cdot 10^{-122} \lor \neg \left(t \leq 3.8 \cdot 10^{-31}\right)\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \]

Alternative 8
Accuracy	67.5%
Cost	978

\[\begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-39} \lor \neg \left(x \leq -7.8 \cdot 10^{-113} \lor \neg \left(x \leq -1.4 \cdot 10^{-161}\right) \land x \leq 9 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \]

Alternative 9
Accuracy	55.7%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-222} \lor \neg \left(x \leq 4 \cdot 10^{-221}\right) \land x \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10
Accuracy	77.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+85} \lor \neg \left(x \leq 1.3 \cdot 10^{-13}\right):\\ \;\;\;\;1 - z \cdot \frac{y}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 11
Accuracy	77.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+86}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \frac{y}{x \cdot x}\\ \end{array} \]

Alternative 12
Accuracy	77.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+85}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \]

Alternative 13
Accuracy	55.6%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-222}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Accuracy	62.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -15000000000 \lor \neg \left(t \leq 1.86 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15
Accuracy	54.3%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023165 
(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)))