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

Percentage Accurate: 89.7% → 96.8%

Time: 10.9s

Alternatives: 14

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

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

MATLAB

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

Initial Program: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

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

MATLAB

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

Alternative 1: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t\_1} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;t\_2 \leq 10^{+284}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 (- INFINITY))
     (* (/ y t_1) (/ z (+ 1.0 x)))
     (if (<= t_2 1e+284) t_2 (/ (+ (/ y t) x) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t_1) * (z / (1.0 + x));
	} else if (t_2 <= 1e+284) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t_1) * (z / (1.0 + x));
	} else if (t_2 <= 1e+284) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t_1) * (z / (1.0 + x))
	elif t_2 <= 1e+284:
		tmp = t_2
	else:
		tmp = ((y / t) + x) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - 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(y / t_1) * Float64(z / Float64(1.0 + x)));
	elseif (t_2 <= 1e+284)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t_1) * (z / (1.0 + x));
	elseif (t_2 <= 1e+284)
		tmp = t_2;
	else
		tmp = ((y / t) + x) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $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[(y / t$95$1), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+284], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

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 #s(literal 1 binary64))) < -inf.0

   1. Initial program 36.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000008e284

   1. Initial program 98.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 1.00000000000000008e284 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 15.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 79.2

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

   5. Applied rewrites 79.2%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+284}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y}{t\_1} \cdot \frac{z}{1 + x}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -4500000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (* (/ y t_1) (/ z (+ 1.0 x))))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -4500000000000.0)
     t_2
     (if (<= t_3 2e-5)
       (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_3 INFINITY) t_2 (/ (+ (/ y t) x) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y / t_1) * (z / (1.0 + x));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -4500000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 2e-5) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y / t_1) * (z / (1.0 + x));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -4500000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 2e-5) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (y / t_1) * (z / (1.0 + x))
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -4500000000000.0:
		tmp = t_2
	elif t_3 <= 2e-5:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	elif t_3 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = ((y / t) + x) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y / t_1) * Float64(z / Float64(1.0 + x)))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -4500000000000.0)
		tmp = t_2;
	elseif (t_3 <= 2e-5)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (y / t_1) * (z / (1.0 + x));
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -4500000000000.0)
		tmp = t_2;
	elseif (t_3 <= 2e-5)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = ((y / t) + x) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t$95$1), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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$3, -4500000000000.0], t$95$2, If[LessEqual[t$95$3, 2e-5], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.5e12 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -4.5e12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000016e-5

   1. Initial program 94.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if 2.00000000000000016e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -4500000000000:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := t \cdot z - x\\ t_3 := \frac{y}{t\_2} \cdot \frac{z}{1 + x}\\ t_4 := \frac{x + \frac{t\_1}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -4500000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{t\_1}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x))
        (t_2 (- (* t z) x))
        (t_3 (* (/ y t_2) (/ z (+ 1.0 x))))
        (t_4 (/ (+ x (/ t_1 t_2)) (+ x 1.0))))
   (if (<= t_4 -4500000000000.0)
     t_3
     (if (<= t_4 2e-5)
       (/ (+ x (/ t_1 (* z t))) (+ x 1.0))
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 INFINITY) t_3 (/ (+ (/ y t) x) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y / t_2) * (z / (1.0 + x));
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4500000000000.0) {
		tmp = t_3;
	} else if (t_4 <= 2e-5) {
		tmp = (x + (t_1 / (z * t))) / (x + 1.0);
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y / t_2) * (z / (1.0 + x));
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4500000000000.0) {
		tmp = t_3;
	} else if (t_4 <= 2e-5) {
		tmp = (x + (t_1 / (z * t))) / (x + 1.0);
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - x
	t_2 = (t * z) - x
	t_3 = (y / t_2) * (z / (1.0 + x))
	t_4 = (x + (t_1 / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -4500000000000.0:
		tmp = t_3
	elif t_4 <= 2e-5:
		tmp = (x + (t_1 / (z * t))) / (x + 1.0)
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = ((y / t) + x) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(y / t_2) * Float64(z / Float64(1.0 + x)))
	t_4 = Float64(Float64(x + Float64(t_1 / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -4500000000000.0)
		tmp = t_3;
	elseif (t_4 <= 2e-5)
		tmp = Float64(Float64(x + Float64(t_1 / Float64(z * t))) / Float64(x + 1.0));
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - x;
	t_2 = (t * z) - x;
	t_3 = (y / t_2) * (z / (1.0 + x));
	t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -4500000000000.0)
		tmp = t_3;
	elseif (t_4 <= 2e-5)
		tmp = (x + (t_1 / (z * t))) / (x + 1.0);
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = ((y / t) + x) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t$95$2), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -4500000000000.0], t$95$3, If[LessEqual[t$95$4, 2e-5], N[(N[(x + N[(t$95$1 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.5e12 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -4.5e12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000016e-5

   1. Initial program 94.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 90.3

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

   5. Applied rewrites 90.3%

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

   7. Applied rewrites 94.7%

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

   if 2.00000000000000016e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -4500000000000:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := t \cdot z - x\\ t_3 := \frac{y}{t\_2} \cdot \frac{z}{1 + x}\\ t_4 := \frac{x + \frac{t\_1}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -4500000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{t\_1}{z \cdot t}}{1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x))
        (t_2 (- (* t z) x))
        (t_3 (* (/ y t_2) (/ z (+ 1.0 x))))
        (t_4 (/ (+ x (/ t_1 t_2)) (+ x 1.0))))
   (if (<= t_4 -4500000000000.0)
     t_3
     (if (<= t_4 2e-5)
       (/ (+ x (/ t_1 (* z t))) 1.0)
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 INFINITY) t_3 (/ (+ (/ y t) x) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y / t_2) * (z / (1.0 + x));
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4500000000000.0) {
		tmp = t_3;
	} else if (t_4 <= 2e-5) {
		tmp = (x + (t_1 / (z * t))) / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y / t_2) * (z / (1.0 + x));
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4500000000000.0) {
		tmp = t_3;
	} else if (t_4 <= 2e-5) {
		tmp = (x + (t_1 / (z * t))) / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - x
	t_2 = (t * z) - x
	t_3 = (y / t_2) * (z / (1.0 + x))
	t_4 = (x + (t_1 / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -4500000000000.0:
		tmp = t_3
	elif t_4 <= 2e-5:
		tmp = (x + (t_1 / (z * t))) / 1.0
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = ((y / t) + x) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(y / t_2) * Float64(z / Float64(1.0 + x)))
	t_4 = Float64(Float64(x + Float64(t_1 / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -4500000000000.0)
		tmp = t_3;
	elseif (t_4 <= 2e-5)
		tmp = Float64(Float64(x + Float64(t_1 / Float64(z * t))) / 1.0);
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - x;
	t_2 = (t * z) - x;
	t_3 = (y / t_2) * (z / (1.0 + x));
	t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -4500000000000.0)
		tmp = t_3;
	elseif (t_4 <= 2e-5)
		tmp = (x + (t_1 / (z * t))) / 1.0;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = ((y / t) + x) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t$95$2), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -4500000000000.0], t$95$3, If[LessEqual[t$95$4, 2e-5], N[(N[(x + N[(t$95$1 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.5e12 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -4.5e12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000016e-5

   1. Initial program 94.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 90.3

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

   5. Applied rewrites 90.3%

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

   7. Applied rewrites 94.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 94.3%

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

   if 2.00000000000000016e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -4500000000000:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t}}{1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{y}{t\_2} \cdot \frac{z}{1 + x}\\ t_4 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -4500000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (* (/ y t_2) (/ z (+ 1.0 x))))
        (t_4 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_4 -4500000000000.0)
     t_3
     (if (<= t_4 2e-5)
       t_1
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 INFINITY) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (y / t_2) * (z / (1.0 + x));
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4500000000000.0) {
		tmp = t_3;
	} else if (t_4 <= 2e-5) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (y / t_2) * (z / (1.0 + x));
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4500000000000.0) {
		tmp = t_3;
	} else if (t_4 <= 2e-5) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (y / t_2) * (z / (1.0 + x))
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -4500000000000.0:
		tmp = t_3
	elif t_4 <= 2e-5:
		tmp = t_1
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(y / t_2) * Float64(z / Float64(1.0 + x)))
	t_4 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -4500000000000.0)
		tmp = t_3;
	elseif (t_4 <= 2e-5)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (y / t_2) * (z / (1.0 + x));
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -4500000000000.0)
		tmp = t_3;
	elseif (t_4 <= 2e-5)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t$95$2), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -4500000000000.0], t$95$3, If[LessEqual[t$95$4, 2e-5], t$95$1, If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, t$95$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 #s(literal 1 binary64))) < -4.5e12 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 81.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -4.5e12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000016e-5 or +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 84.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 88.8

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

   5. Applied rewrites 88.8%

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

   if 2.00000000000000016e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.9

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

   5. Applied rewrites 98.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -4500000000000:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{t \cdot z - x} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_3 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 10^{+284}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_2}}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_3 2e-5)
     t_1
     (if (<= t_3 2.0)
       (/ (- x (/ x t_2)) (+ x 1.0))
       (if (<= t_3 1e+284) (/ (* y (/ z t_2)) 1.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= 2e-5) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_3 <= 1e+284) {
		tmp = (y * (z / t_2)) / 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((y / t) + x) / (x + 1.0d0)
    t_2 = (t * z) - x
    t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_3 <= 2d-5) then
        tmp = t_1
    else if (t_3 <= 2.0d0) then
        tmp = (x - (x / t_2)) / (x + 1.0d0)
    else if (t_3 <= 1d+284) then
        tmp = (y * (z / t_2)) / 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= 2e-5) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_3 <= 1e+284) {
		tmp = (y * (z / t_2)) / 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_3 <= 2e-5:
		tmp = t_1
	elif t_3 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_3 <= 1e+284:
		tmp = (y * (z / t_2)) / 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= 2e-5)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_3 <= 1e+284)
		tmp = Float64(Float64(y * Float64(z / t_2)) / 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= 2e-5)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_3 <= 1e+284)
		tmp = (y * (z / t_2)) / 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-5], t$95$1, If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+284], N[(N[(y * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], t$95$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 #s(literal 1 binary64))) < 2.00000000000000016e-5 or 1.00000000000000008e284 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 76.9

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

   5. Applied rewrites 76.9%

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

   if 2.00000000000000016e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000008e284

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

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

   7. Applied rewrites 53.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 44.2%

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

   11. Taylor expanded in y around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 N/A

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

       5. lower-*.f64 76.8

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

   13. Applied rewrites 76.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+284}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t \cdot z - x}}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_3 \leq 0.9999999999986179:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 10^{+284}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_2}}{1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_3 0.9999999999986179)
     t_1
     (if (<= t_3 2.0) 1.0 (if (<= t_3 1e+284) (/ (* y (/ z t_2)) 1.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= 0.9999999999986179) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 1e+284) {
		tmp = (y * (z / t_2)) / 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((y / t) + x) / (x + 1.0d0)
    t_2 = (t * z) - x
    t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_3 <= 0.9999999999986179d0) then
        tmp = t_1
    else if (t_3 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_3 <= 1d+284) then
        tmp = (y * (z / t_2)) / 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= 0.9999999999986179) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 1e+284) {
		tmp = (y * (z / t_2)) / 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_3 <= 0.9999999999986179:
		tmp = t_1
	elif t_3 <= 2.0:
		tmp = 1.0
	elif t_3 <= 1e+284:
		tmp = (y * (z / t_2)) / 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= 0.9999999999986179)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 1e+284)
		tmp = Float64(Float64(y * Float64(z / t_2)) / 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= 0.9999999999986179)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 1e+284)
		tmp = (y * (z / t_2)) / 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 0.9999999999986179], t$95$1, If[LessEqual[t$95$3, 2.0], 1.0, If[LessEqual[t$95$3, 1e+284], N[(N[(y * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], t$95$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 #s(literal 1 binary64))) < 0.999999999998617883 or 1.00000000000000008e284 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if 0.999999999998617883 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.8%

      \[\leadsto \color{blue}{1} \]

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000008e284

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

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

   7. Applied rewrites 53.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 44.2%

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

   11. Taylor expanded in y around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 N/A

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

       5. lower-*.f64 76.8

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

   13. Applied rewrites 76.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 0.9999999999986179:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+284}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t \cdot z - x}}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999986179:\\ \;\;\;\;\frac{x}{1 + x}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2.5e-187)
     (/ y t)
     (if (<= t_1 0.9999999999986179)
       (/ x (+ 1.0 x))
       (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2.5e-187) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999986179) {
		tmp = x / (1.0 + x);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= (-2.5d-187)) then
        tmp = y / t
    else if (t_1 <= 0.9999999999986179d0) then
        tmp = x / (1.0d0 + x)
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

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 tmp;
	if (t_1 <= -2.5e-187) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999986179) {
		tmp = x / (1.0 + x);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -2.5e-187:
		tmp = y / t
	elif t_1 <= 0.9999999999986179:
		tmp = x / (1.0 + x)
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

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))
	tmp = 0.0
	if (t_1 <= -2.5e-187)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999999986179)
		tmp = Float64(x / Float64(1.0 + x));
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -2.5e-187)
		tmp = y / t;
	elseif (t_1 <= 0.9999999999986179)
		tmp = x / (1.0 + x);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

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]}, If[LessEqual[t$95$1, -2.5e-187], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999986179], N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $MachinePrecision]]]]]

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 #s(literal 1 binary64))) < -2.4999999999999998e-187 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 78.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 44.9

         \[\leadsto \color{blue}{\frac{y}{t}} \]

   5. Applied rewrites 44.9%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if -2.4999999999999998e-187 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999998617883

   1. Initial program 94.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if 0.999999999998617883 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-1, x, 1\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2.5e-187)
     (/ y t)
     (if (<= t_1 1e-12)
       (* (fma -1.0 x 1.0) x)
       (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2.5e-187) {
		tmp = y / t;
	} else if (t_1 <= 1e-12) {
		tmp = fma(-1.0, x, 1.0) * x;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Julia

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))
	tmp = 0.0
	if (t_1 <= -2.5e-187)
		tmp = Float64(y / t);
	elseif (t_1 <= 1e-12)
		tmp = Float64(fma(-1.0, x, 1.0) * x);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

Wolfram

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]}, If[LessEqual[t$95$1, -2.5e-187], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 1e-12], N[(N[(-1.0 * x + 1.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $MachinePrecision]]]]]

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 #s(literal 1 binary64))) < -2.4999999999999998e-187 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 78.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 44.9

         \[\leadsto \color{blue}{\frac{y}{t}} \]

   5. Applied rewrites 44.9%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if -2.4999999999999998e-187 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13

   1. Initial program 94.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

   4. Applied rewrites 64.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 65.4

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

   7. Applied rewrites 65.4%

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

   8. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot x\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 65.4%

       \[\leadsto \mathsf{fma}\left(-1, x, 1\right) \cdot \color{blue}{x} \]

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 96.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-1, x, 1\right) \cdot x\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999986179:\\ \;\;\;\;\frac{x}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2.5e-187)
     (/ y t)
     (if (<= t_1 0.9999999999986179)
       (/ x (+ 1.0 x))
       (fma (/ z (fma x x x)) (- y) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2.5e-187) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999986179) {
		tmp = x / (1.0 + x);
	} else {
		tmp = fma((z / fma(x, x, x)), -y, 1.0);
	}
	return tmp;
}

Julia

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))
	tmp = 0.0
	if (t_1 <= -2.5e-187)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999999986179)
		tmp = Float64(x / Float64(1.0 + x));
	else
		tmp = fma(Float64(z / fma(x, x, x)), Float64(-y), 1.0);
	end
	return tmp
end

Wolfram

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]}, If[LessEqual[t$95$1, -2.5e-187], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999986179], N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(x * x + x), $MachinePrecision]), $MachinePrecision] * (-y) + 1.0), $MachinePrecision]]]]

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 #s(literal 1 binary64))) < -2.4999999999999998e-187

   1. Initial program 86.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 49.5

         \[\leadsto \color{blue}{\frac{y}{t}} \]

   5. Applied rewrites 49.5%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if -2.4999999999999998e-187 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999998617883

   1. Initial program 94.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if 0.999999999998617883 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 93.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac N/A

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

      6. associate-/r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. *-rgt-identity N/A

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

      20. lower-fma.f64 86.9

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

   5. Applied rewrites 86.9%

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

   7. Applied rewrites 86.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 0.9999999999986179:\\ \;\;\;\;\frac{x}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-5} \lor \neg \left(t\_1 \leq 2\right):\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (or (<= t_1 2e-5) (not (<= t_1 2.0))) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= 2e-5) || !(t_1 <= 2.0)) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if ((t_1 <= 2d-5) .or. (.not. (t_1 <= 2.0d0))) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

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 tmp;
	if ((t_1 <= 2e-5) || !(t_1 <= 2.0)) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if (t_1 <= 2e-5) or not (t_1 <= 2.0):
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

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))
	tmp = 0.0
	if ((t_1 <= 2e-5) || !(t_1 <= 2.0))
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if ((t_1 <= 2e-5) || ~((t_1 <= 2.0)))
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

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]}, If[Or[LessEqual[t$95$1, 2e-5], N[Not[LessEqual[t$95$1, 2.0]], $MachinePrecision]], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000016e-5 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 83.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 39.6

         \[\leadsto \color{blue}{\frac{y}{t}} \]

   5. Applied rewrites 39.6%

      \[\leadsto \color{blue}{\frac{y}{t}} \]

   if 2.00000000000000016e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2\right):\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) 2e-5)
   (/ (+ (/ y t) x) 1.0)
   (fma (/ z (fma x x x)) (- y) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)) <= 2e-5) {
		tmp = ((y / t) + x) / 1.0;
	} else {
		tmp = fma((z / fma(x, x, x)), -y, 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) <= 2e-5)
		tmp = Float64(Float64(Float64(y / t) + x) / 1.0);
	else
		tmp = fma(Float64(z / fma(x, x, x)), Float64(-y), 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[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], 2e-5], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / 1.0), $MachinePrecision], N[(N[(z / N[(x * x + x), $MachinePrecision]), $MachinePrecision] * (-y) + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000016e-5

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 76.6

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

   7. Applied rewrites 76.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 73.2%

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

   if 2.00000000000000016e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 93.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac N/A

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

      6. associate-/r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. *-rgt-identity N/A

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

      20. lower-fma.f64 86.8

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

   5. Applied rewrites 86.8%

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

   7. Applied rewrites 86.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-92} \lor \neg \left(t \leq 7.8 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e-92) (not (<= t 7.8e-35)))
   (/ (+ (/ y t) x) (+ x 1.0))
   (fma (/ z (fma x x x)) (- y) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e-92) || !(t <= 7.8e-35)) {
		tmp = ((y / t) + x) / (x + 1.0);
	} else {
		tmp = fma((z / fma(x, x, x)), -y, 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e-92) || !(t <= 7.8e-35))
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	else
		tmp = fma(Float64(z / fma(x, x, x)), Float64(-y), 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e-92], N[Not[LessEqual[t, 7.8e-35]], $MachinePrecision]], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(x * x + x), $MachinePrecision]), $MachinePrecision] * (-y) + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000011e-92 or 7.79999999999999961e-35 < t

   1. Initial program 91.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -5.00000000000000011e-92 < t < 7.79999999999999961e-35

   1. Initial program 93.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac N/A

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

      6. associate-/r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. *-rgt-identity N/A

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

      20. lower-fma.f64 83.8

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

   5. Applied rewrites 83.8%

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

   7. Applied rewrites 83.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-92} \lor \neg \left(t \leq 7.8 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.2% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

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

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 91.9%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 55.7%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024342 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

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