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

Average Error: 7.2 → 2.5

Time: 20.6s

Precision: binary64

Cost: 6096

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ t_2 := \frac{y}{t} + x\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t_2}{x + 1}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot y}{\left(\left(x + t \cdot z\right) - x \cdot 2\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{t_2 - \frac{x}{t \cdot z}}{x + 1}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+268}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \left(-\frac{-\left(\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}\right)}{t}\right)\\ \end{array} \]

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 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
        (t_2 (+ (/ y t) x)))
   (if (<= t_1 (- INFINITY))
     (/ t_2 (+ x 1.0))
     (if (<= t_1 -1e+69)
       (/ (* z y) (* (- (+ x (* t z)) (* x 2.0)) (+ x 1.0)))
       (if (<= t_1 5e-79)
         (/ (- t_2 (/ x (* t z))) (+ x 1.0))
         (if (<= t_1 2e+268)
           t_1
           (+
            (/ x (+ x 1.0))
            (- (/ (- (- (/ y (+ x 1.0)) (/ x (* z (+ x 1.0))))) t)))))))))

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 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double t_2 = (y / t) + x;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2 / (x + 1.0);
	} else if (t_1 <= -1e+69) {
		tmp = (z * y) / (((x + (t * z)) - (x * 2.0)) * (x + 1.0));
	} else if (t_1 <= 5e-79) {
		tmp = (t_2 - (x / (t * z))) / (x + 1.0);
	} else if (t_1 <= 2e+268) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + -(-((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	}
	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 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double t_2 = (y / t) + x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2 / (x + 1.0);
	} else if (t_1 <= -1e+69) {
		tmp = (z * y) / (((x + (t * z)) - (x * 2.0)) * (x + 1.0));
	} else if (t_1 <= 5e-79) {
		tmp = (t_2 - (x / (t * z))) / (x + 1.0);
	} else if (t_1 <= 2e+268) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + -(-((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	}
	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 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	t_2 = (y / t) + x
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2 / (x + 1.0)
	elif t_1 <= -1e+69:
		tmp = (z * y) / (((x + (t * z)) - (x * 2.0)) * (x + 1.0))
	elif t_1 <= 5e-79:
		tmp = (t_2 - (x / (t * z))) / (x + 1.0)
	elif t_1 <= 2e+268:
		tmp = t_1
	else:
		tmp = (x / (x + 1.0)) + -(-((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t)
	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(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	t_2 = Float64(Float64(y / t) + x)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_2 / Float64(x + 1.0));
	elseif (t_1 <= -1e+69)
		tmp = Float64(Float64(z * y) / Float64(Float64(Float64(x + Float64(t * z)) - Float64(x * 2.0)) * Float64(x + 1.0)));
	elseif (t_1 <= 5e-79)
		tmp = Float64(Float64(t_2 - Float64(x / Float64(t * z))) / Float64(x + 1.0));
	elseif (t_1 <= 2e+268)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(-Float64(Float64(-Float64(Float64(y / Float64(x + 1.0)) - Float64(x / Float64(z * Float64(x + 1.0))))) / t)));
	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 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	t_2 = (y / t) + x;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2 / (x + 1.0);
	elseif (t_1 <= -1e+69)
		tmp = (z * y) / (((x + (t * z)) - (x * 2.0)) * (x + 1.0));
	elseif (t_1 <= 5e-79)
		tmp = (t_2 - (x / (t * z))) / (x + 1.0);
	elseif (t_1 <= 2e+268)
		tmp = t_1;
	else
		tmp = (x / (x + 1.0)) + -(-((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t$95$2 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+69], N[(N[(z * y), $MachinePrecision] / N[(N[(N[(x + N[(t * z), $MachinePrecision]), $MachinePrecision] - N[(x * 2.0), $MachinePrecision]), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-79], N[(N[(t$95$2 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+268], t$95$1, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + (-N[((-N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) / t), $MachinePrecision])), $MachinePrecision]]]]]]]

Target

Original	7.2
Target	0.3
Herbie	2.5

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

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)) < -inf.0

   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

      [Start] 64.0	\[ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
      rational_best.json-simplify-2 [=>] 64.0	\[ \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Taylor expanded in z around inf 22.3

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -1.0000000000000001e69

   1. Initial program 0.4

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

   2. Simplified 0.4

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

      [Start] 0.4	\[ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
      rational_best.json-simplify-2 [=>] 0.4	\[ \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Applied egg-rr 0.4

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

   4. Taylor expanded in y around inf 0.4

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

   5. Simplified 0.4

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

      [Start] 0.4	\[ \frac{y \cdot z}{\left(1 + x\right) \cdot \left(\left(t \cdot z + x\right) - 2 \cdot x\right)} \]
      rational_best.json-simplify-2 [=>] 0.4	\[ \frac{\color{blue}{z \cdot y}}{\left(1 + x\right) \cdot \left(\left(t \cdot z + x\right) - 2 \cdot x\right)} \]
      rational_best.json-simplify-2 [=>] 0.4	\[ \frac{z \cdot y}{\color{blue}{\left(\left(t \cdot z + x\right) - 2 \cdot x\right) \cdot \left(1 + x\right)}} \]
      rational_best.json-simplify-1 [=>] 0.4	\[ \frac{z \cdot y}{\left(\color{blue}{\left(x + t \cdot z\right)} - 2 \cdot x\right) \cdot \left(1 + x\right)} \]
      rational_best.json-simplify-2 [=>] 0.4	\[ \frac{z \cdot y}{\left(\left(x + t \cdot z\right) - \color{blue}{x \cdot 2}\right) \cdot \left(1 + x\right)} \]
      rational_best.json-simplify-1 [=>] 0.4	\[ \frac{z \cdot y}{\left(\left(x + t \cdot z\right) - x \cdot 2\right) \cdot \color{blue}{\left(x + 1\right)}} \]

   if -1.0000000000000001e69 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 4.99999999999999999e-79

   1. Initial program 2.4

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

   2. Simplified 2.4

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

      [Start] 2.4	\[ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
      rational_best.json-simplify-2 [=>] 2.4	\[ \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Taylor expanded in t around inf 4.7

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

   if 4.99999999999999999e-79 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.9999999999999999e268

   1. Initial program 0.1

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

   if 1.9999999999999999e268 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 58.9

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

   2. Simplified 58.9

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

      [Start] 58.9	\[ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
      rational_best.json-simplify-2 [=>] 58.9	\[ \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Taylor expanded in t around inf 10.8

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

   4. Taylor expanded in t around -inf 10.1

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

   5. Simplified 10.1

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

      [Start] 10.1	\[ -1 \cdot \frac{-1 \cdot \frac{y}{1 + x} - -1 \cdot \frac{x}{\left(1 + x\right) \cdot z}}{t} + \frac{x}{1 + x} \]
      rational_best.json-simplify-1 [=>] 10.1	\[ \color{blue}{\frac{x}{1 + x} + -1 \cdot \frac{-1 \cdot \frac{y}{1 + x} - -1 \cdot \frac{x}{\left(1 + x\right) \cdot z}}{t}} \]
      rational_best.json-simplify-1 [<=] 10.1	\[ \frac{x}{\color{blue}{x + 1}} + -1 \cdot \frac{-1 \cdot \frac{y}{1 + x} - -1 \cdot \frac{x}{\left(1 + x\right) \cdot z}}{t} \]
      rational_best.json-simplify-2 [=>] 10.1	\[ \frac{x}{x + 1} + \color{blue}{\frac{-1 \cdot \frac{y}{1 + x} - -1 \cdot \frac{x}{\left(1 + x\right) \cdot z}}{t} \cdot -1} \]
      rational_best.json-simplify-12 [=>] 10.1	\[ \frac{x}{x + 1} + \color{blue}{\left(-\frac{-1 \cdot \frac{y}{1 + x} - -1 \cdot \frac{x}{\left(1 + x\right) \cdot z}}{t}\right)} \]
      rational_best.json-simplify-2 [=>] 10.1	\[ \frac{x}{x + 1} + \left(-\frac{-1 \cdot \frac{y}{1 + x} - \color{blue}{\frac{x}{\left(1 + x\right) \cdot z} \cdot -1}}{t}\right) \]
      rational_best.json-simplify-48 [=>] 10.1	\[ \frac{x}{x + 1} + \left(-\frac{\color{blue}{-1 \cdot \left(\frac{y}{1 + x} - \frac{x}{\left(1 + x\right) \cdot z}\right)}}{t}\right) \]
      rational_best.json-simplify-2 [=>] 10.1	\[ \frac{x}{x + 1} + \left(-\frac{\color{blue}{\left(\frac{y}{1 + x} - \frac{x}{\left(1 + x\right) \cdot z}\right) \cdot -1}}{t}\right) \]
      rational_best.json-simplify-12 [=>] 10.1	\[ \frac{x}{x + 1} + \left(-\frac{\color{blue}{-\left(\frac{y}{1 + x} - \frac{x}{\left(1 + x\right) \cdot z}\right)}}{t}\right) \]
      rational_best.json-simplify-1 [<=] 10.1	\[ \frac{x}{x + 1} + \left(-\frac{-\left(\frac{y}{\color{blue}{x + 1}} - \frac{x}{\left(1 + x\right) \cdot z}\right)}{t}\right) \]
      rational_best.json-simplify-2 [=>] 10.1	\[ \frac{x}{x + 1} + \left(-\frac{-\left(\frac{y}{x + 1} - \frac{x}{\color{blue}{z \cdot \left(1 + x\right)}}\right)}{t}\right) \]
      rational_best.json-simplify-1 [<=] 10.1	\[ \frac{x}{x + 1} + \left(-\frac{-\left(\frac{y}{x + 1} - \frac{x}{z \cdot \color{blue}{\left(x + 1\right)}}\right)}{t}\right) \]

3. Recombined 5 regimes into one program.

4. Final simplification 2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot y}{\left(\left(x + t \cdot z\right) - x \cdot 2\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{\left(\frac{y}{t} + x\right) - \frac{x}{t \cdot z}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{+268}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \left(-\frac{-\left(\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}\right)}{t}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.6
Cost	5840

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ t_2 := \frac{y}{t} + x\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t_2}{x + 1}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot y}{\left(\left(x + t \cdot z\right) - x \cdot 2\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{t_2 - \frac{x}{t \cdot z}}{x + 1}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+268}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \left(-\frac{-\left(\frac{y}{x + 1} - \frac{x}{z}\right)}{t}\right)\\ \end{array} \]

Alternative 2
Error	2.6
Cost	5712

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ t_2 := \frac{y}{t} + x\\ t_3 := \frac{t_2}{x + 1}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot y}{\left(\left(x + t \cdot z\right) - x \cdot 2\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{t_2 - \frac{x}{t \cdot z}}{x + 1}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+268}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	25.2
Cost	1372

\[\begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := \frac{y}{\left(1 + x\right) \cdot t}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-147}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+305}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	24.7
Cost	1372

\[\begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := \frac{y}{\left(1 + x\right) \cdot t}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;1 + z \cdot \left(-\frac{y}{x}\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	12.3
Cost	1032

\[\begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{if}\;t \leq -440000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-68}:\\ \;\;\;\;1 + z \cdot \left(-\frac{y}{x \cdot \left(x - -1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	15.1
Cost	840

\[\begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-22}:\\ \;\;\;\;1 + z \cdot \left(-\frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	20.8
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	20.6
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	27.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-168}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10
Error	28.4
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023088 
(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)))