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

Percentage Accurate: 89.3% → 95.6%

Time: 10.8s

Alternatives: 15

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: 89.3% 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: 95.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (* (- -1.0 x) (- x (* t z)))) z)
     (if (<= t_1 5e+167) t_1 (/ (+ (/ y t) x) (- x -1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z;
	} else if (t_1 <= 5e+167) {
		tmp = t_1;
	} 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z;
	} else if (t_1 <= 5e+167) {
		tmp = t_1;
	} else {
		tmp = ((y / t) + x) / (x - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z
	elif t_1 <= 5e+167:
		tmp = t_1
	else:
		tmp = ((y / t) + x) / (x - -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z)))) * z);
	elseif (t_1 <= 5e+167)
		tmp = t_1;
	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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z;
	elseif (t_1 <= 5e+167)
		tmp = t_1;
	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[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+167], t$95$1, 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 48.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 48.8

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

   5. Applied rewrites 48.8%

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

   7. Applied rewrites 80.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999997e167

   1. Initial program 99.4%

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

   if 4.9999999999999997e167 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   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 z around inf

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

      1. lower-/.f64 87.2

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

   5. Applied rewrites 87.2%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-1 - x\right) \cdot \left(x - t \cdot z\right)\\ t_2 := \frac{z \cdot y}{t\_1}\\ t_3 := t \cdot z - x\\ t_4 := \frac{x - \frac{x - z \cdot y}{t\_3}}{x - -1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;\frac{y}{t\_1} \cdot z\\ \mathbf{elif}\;t\_4 \leq -20000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x - -1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_3}}{x - -1}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- -1.0 x) (- x (* t z))))
        (t_2 (/ (* z y) t_1))
        (t_3 (- (* t z) x))
        (t_4 (/ (- x (/ (- x (* z y)) t_3)) (- x -1.0))))
   (if (<= t_4 (- INFINITY))
     (* (/ y t_1) z)
     (if (<= t_4 -20000000000.0)
       t_2
       (if (<= t_4 5e-6)
         (/ (- x (/ (- (/ x z) y) t)) (- x -1.0))
         (if (<= t_4 2.0)
           (/ (- x (/ x t_3)) (- x -1.0))
           (if (<= t_4 5e+167) t_2 (/ (+ (/ y t) x) (- x -1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-1.0 - x) * (x - (t * z));
	double t_2 = (z * y) / t_1;
	double t_3 = (t * z) - x;
	double t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (y / t_1) * z;
	} else if (t_4 <= -20000000000.0) {
		tmp = t_2;
	} else if (t_4 <= 5e-6) {
		tmp = (x - (((x / z) - y) / t)) / (x - -1.0);
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_3)) / (x - -1.0);
	} else if (t_4 <= 5e+167) {
		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 = (-1.0 - x) * (x - (t * z));
	double t_2 = (z * y) / t_1;
	double t_3 = (t * z) - x;
	double t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t_1) * z;
	} else if (t_4 <= -20000000000.0) {
		tmp = t_2;
	} else if (t_4 <= 5e-6) {
		tmp = (x - (((x / z) - y) / t)) / (x - -1.0);
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_3)) / (x - -1.0);
	} else if (t_4 <= 5e+167) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (x - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-1.0 - x) * (x - (t * z))
	t_2 = (z * y) / t_1
	t_3 = (t * z) - x
	t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = (y / t_1) * z
	elif t_4 <= -20000000000.0:
		tmp = t_2
	elif t_4 <= 5e-6:
		tmp = (x - (((x / z) - y) / t)) / (x - -1.0)
	elif t_4 <= 2.0:
		tmp = (x - (x / t_3)) / (x - -1.0)
	elif t_4 <= 5e+167:
		tmp = t_2
	else:
		tmp = ((y / t) + x) / (x - -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z)))
	t_2 = Float64(Float64(z * y) / t_1)
	t_3 = Float64(Float64(t * z) - x)
	t_4 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_3)) / Float64(x - -1.0))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(y / t_1) * z);
	elseif (t_4 <= -20000000000.0)
		tmp = t_2;
	elseif (t_4 <= 5e-6)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x - -1.0));
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_3)) / Float64(x - -1.0));
	elseif (t_4 <= 5e+167)
		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 = (-1.0 - x) * (x - (t * z));
	t_2 = (z * y) / t_1;
	t_3 = (t * z) - x;
	t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = (y / t_1) * z;
	elseif (t_4 <= -20000000000.0)
		tmp = t_2;
	elseif (t_4 <= 5e-6)
		tmp = (x - (((x / z) - y) / t)) / (x - -1.0);
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_3)) / (x - -1.0);
	elseif (t_4 <= 5e+167)
		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[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(y / t$95$1), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$4, -20000000000.0], t$95$2, If[LessEqual[t$95$4, 5e-6], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+167], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 48.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 48.8

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

   5. Applied rewrites 48.8%

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

   7. Applied rewrites 80.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2e10 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999997e167

   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 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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if -2e10 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000041e-6

   1. Initial program 98.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if 5.00000000000000041e-6 < (/.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 99.7

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

   5. Applied rewrites 99.7%

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

   if 4.9999999999999997e167 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   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 z around inf

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

      1. lower-/.f64 87.2

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

   5. Applied rewrites 87.2%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -20000000000:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-1 - x\right) \cdot \left(x - t \cdot z\right)\\ t_2 := \frac{z \cdot y}{t\_1}\\ t_3 := t \cdot z - x\\ t_4 := \frac{x - \frac{x - z \cdot y}{t\_3}}{x - -1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;\frac{y}{t\_1} \cdot z\\ \mathbf{elif}\;t\_4 \leq -20000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{z \cdot y - x}{t \cdot z} + x}{x - -1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_3}}{x - -1}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- -1.0 x) (- x (* t z))))
        (t_2 (/ (* z y) t_1))
        (t_3 (- (* t z) x))
        (t_4 (/ (- x (/ (- x (* z y)) t_3)) (- x -1.0))))
   (if (<= t_4 (- INFINITY))
     (* (/ y t_1) z)
     (if (<= t_4 -20000000000.0)
       t_2
       (if (<= t_4 5e-6)
         (/ (+ (/ (- (* z y) x) (* t z)) x) (- x -1.0))
         (if (<= t_4 2.0)
           (/ (- x (/ x t_3)) (- x -1.0))
           (if (<= t_4 5e+167) t_2 (/ (+ (/ y t) x) (- x -1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-1.0 - x) * (x - (t * z));
	double t_2 = (z * y) / t_1;
	double t_3 = (t * z) - x;
	double t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (y / t_1) * z;
	} else if (t_4 <= -20000000000.0) {
		tmp = t_2;
	} else if (t_4 <= 5e-6) {
		tmp = ((((z * y) - x) / (t * z)) + x) / (x - -1.0);
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_3)) / (x - -1.0);
	} else if (t_4 <= 5e+167) {
		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 = (-1.0 - x) * (x - (t * z));
	double t_2 = (z * y) / t_1;
	double t_3 = (t * z) - x;
	double t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t_1) * z;
	} else if (t_4 <= -20000000000.0) {
		tmp = t_2;
	} else if (t_4 <= 5e-6) {
		tmp = ((((z * y) - x) / (t * z)) + x) / (x - -1.0);
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_3)) / (x - -1.0);
	} else if (t_4 <= 5e+167) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (x - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-1.0 - x) * (x - (t * z))
	t_2 = (z * y) / t_1
	t_3 = (t * z) - x
	t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = (y / t_1) * z
	elif t_4 <= -20000000000.0:
		tmp = t_2
	elif t_4 <= 5e-6:
		tmp = ((((z * y) - x) / (t * z)) + x) / (x - -1.0)
	elif t_4 <= 2.0:
		tmp = (x - (x / t_3)) / (x - -1.0)
	elif t_4 <= 5e+167:
		tmp = t_2
	else:
		tmp = ((y / t) + x) / (x - -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z)))
	t_2 = Float64(Float64(z * y) / t_1)
	t_3 = Float64(Float64(t * z) - x)
	t_4 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_3)) / Float64(x - -1.0))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(y / t_1) * z);
	elseif (t_4 <= -20000000000.0)
		tmp = t_2;
	elseif (t_4 <= 5e-6)
		tmp = Float64(Float64(Float64(Float64(Float64(z * y) - x) / Float64(t * z)) + x) / Float64(x - -1.0));
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_3)) / Float64(x - -1.0));
	elseif (t_4 <= 5e+167)
		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 = (-1.0 - x) * (x - (t * z));
	t_2 = (z * y) / t_1;
	t_3 = (t * z) - x;
	t_4 = (x - ((x - (z * y)) / t_3)) / (x - -1.0);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = (y / t_1) * z;
	elseif (t_4 <= -20000000000.0)
		tmp = t_2;
	elseif (t_4 <= 5e-6)
		tmp = ((((z * y) - x) / (t * z)) + x) / (x - -1.0);
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_3)) / (x - -1.0);
	elseif (t_4 <= 5e+167)
		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[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(y / t$95$1), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$4, -20000000000.0], t$95$2, If[LessEqual[t$95$4, 5e-6], N[(N[(N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+167], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 48.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 48.8

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

   5. Applied rewrites 48.8%

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

   7. Applied rewrites 80.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2e10 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999997e167

   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 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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 98.2

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

   5. Applied rewrites 98.2%

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

   if -2e10 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000041e-6

   1. Initial program 98.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 96.4

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

   5. Applied rewrites 96.4%

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

   if 5.00000000000000041e-6 < (/.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 99.7

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

   5. Applied rewrites 99.7%

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

   if 4.9999999999999997e167 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   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 z around inf

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

      1. lower-/.f64 87.2

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

   5. Applied rewrites 87.2%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -20000000000:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{z \cdot y - x}{t \cdot z} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := \left(-1 - x\right) \cdot \left(x - t \cdot z\right)\\ t_3 := \frac{z \cdot y}{t\_2}\\ t_4 := t \cdot z - x\\ t_5 := \frac{x - \frac{x - z \cdot y}{t\_4}}{x - -1}\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;\frac{y}{t\_2} \cdot z\\ \mathbf{elif}\;t\_5 \leq -1:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_5 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_4}}{x - -1}\\ \mathbf{elif}\;t\_5 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (* (- -1.0 x) (- x (* t z))))
        (t_3 (/ (* z y) t_2))
        (t_4 (- (* t z) x))
        (t_5 (/ (- x (/ (- x (* z y)) t_4)) (- x -1.0))))
   (if (<= t_5 (- INFINITY))
     (* (/ y t_2) z)
     (if (<= t_5 -1.0)
       t_3
       (if (<= t_5 2e-27)
         t_1
         (if (<= t_5 2.0)
           (/ (- x (/ x t_4)) (- x -1.0))
           (if (<= t_5 5e+167) 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 = (-1.0 - x) * (x - (t * z));
	double t_3 = (z * y) / t_2;
	double t_4 = (t * z) - x;
	double t_5 = (x - ((x - (z * y)) / t_4)) / (x - -1.0);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = (y / t_2) * z;
	} else if (t_5 <= -1.0) {
		tmp = t_3;
	} else if (t_5 <= 2e-27) {
		tmp = t_1;
	} else if (t_5 <= 2.0) {
		tmp = (x - (x / t_4)) / (x - -1.0);
	} else if (t_5 <= 5e+167) {
		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 = (-1.0 - x) * (x - (t * z));
	double t_3 = (z * y) / t_2;
	double t_4 = (t * z) - x;
	double t_5 = (x - ((x - (z * y)) / t_4)) / (x - -1.0);
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t_2) * z;
	} else if (t_5 <= -1.0) {
		tmp = t_3;
	} else if (t_5 <= 2e-27) {
		tmp = t_1;
	} else if (t_5 <= 2.0) {
		tmp = (x - (x / t_4)) / (x - -1.0);
	} else if (t_5 <= 5e+167) {
		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 = (-1.0 - x) * (x - (t * z))
	t_3 = (z * y) / t_2
	t_4 = (t * z) - x
	t_5 = (x - ((x - (z * y)) / t_4)) / (x - -1.0)
	tmp = 0
	if t_5 <= -math.inf:
		tmp = (y / t_2) * z
	elif t_5 <= -1.0:
		tmp = t_3
	elif t_5 <= 2e-27:
		tmp = t_1
	elif t_5 <= 2.0:
		tmp = (x - (x / t_4)) / (x - -1.0)
	elif t_5 <= 5e+167:
		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(-1.0 - x) * Float64(x - Float64(t * z)))
	t_3 = Float64(Float64(z * y) / t_2)
	t_4 = Float64(Float64(t * z) - x)
	t_5 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_4)) / Float64(x - -1.0))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(y / t_2) * z);
	elseif (t_5 <= -1.0)
		tmp = t_3;
	elseif (t_5 <= 2e-27)
		tmp = t_1;
	elseif (t_5 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_4)) / Float64(x - -1.0));
	elseif (t_5 <= 5e+167)
		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 = (-1.0 - x) * (x - (t * z));
	t_3 = (z * y) / t_2;
	t_4 = (t * z) - x;
	t_5 = (x - ((x - (z * y)) / t_4)) / (x - -1.0);
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = (y / t_2) * z;
	elseif (t_5 <= -1.0)
		tmp = t_3;
	elseif (t_5 <= 2e-27)
		tmp = t_1;
	elseif (t_5 <= 2.0)
		tmp = (x - (x / t_4)) / (x - -1.0);
	elseif (t_5 <= 5e+167)
		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[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * y), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(y / t$95$2), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$5, -1.0], t$95$3, If[LessEqual[t$95$5, 2e-27], t$95$1, If[LessEqual[t$95$5, 2.0], N[(N[(x - N[(x / t$95$4), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 5e+167], t$95$3, t$95$1]]]]]]]]]]

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))) < -inf.0

   1. Initial program 48.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 48.8

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

   5. Applied rewrites 48.8%

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

   7. Applied rewrites 80.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999997e167

   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 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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 95.5

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

   5. Applied rewrites 95.5%

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

   if -1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.0000000000000001e-27 or 4.9999999999999997e167 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 80.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 81.3

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

   5. Applied rewrites 81.3%

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

   if 2.0000000000000001e-27 < (/.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 99.0

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

   5. Applied rewrites 99.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -1:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ t_3 := \left(-1 - x\right) \cdot \left(x - t \cdot z\right)\\ t_4 := \frac{z \cdot y}{t\_3}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t\_3} \cdot z\\ \mathbf{elif}\;t\_2 \leq -1:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 0.9999999999965637:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)))
        (t_3 (* (- -1.0 x) (- x (* t z))))
        (t_4 (/ (* z y) t_3)))
   (if (<= t_2 (- INFINITY))
     (* (/ y t_3) z)
     (if (<= t_2 -1.0)
       t_4
       (if (<= t_2 0.9999999999965637)
         t_1
         (if (<= t_2 2.0) 1.0 (if (<= t_2 5e+167) t_4 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double t_3 = (-1.0 - x) * (x - (t * z));
	double t_4 = (z * y) / t_3;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t_3) * z;
	} else if (t_2 <= -1.0) {
		tmp = t_4;
	} else if (t_2 <= 0.9999999999965637) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+167) {
		tmp = t_4;
	} 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double t_3 = (-1.0 - x) * (x - (t * z));
	double t_4 = (z * y) / t_3;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t_3) * z;
	} else if (t_2 <= -1.0) {
		tmp = t_4;
	} else if (t_2 <= 0.9999999999965637) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+167) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x - -1.0)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	t_3 = (-1.0 - x) * (x - (t * z))
	t_4 = (z * y) / t_3
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t_3) * z
	elif t_2 <= -1.0:
		tmp = t_4
	elif t_2 <= 0.9999999999965637:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	elif t_2 <= 5e+167:
		tmp = t_4
	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(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	t_3 = Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z)))
	t_4 = Float64(Float64(z * y) / t_3)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t_3) * z);
	elseif (t_2 <= -1.0)
		tmp = t_4;
	elseif (t_2 <= 0.9999999999965637)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+167)
		tmp = t_4;
	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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	t_3 = (-1.0 - x) * (x - (t * z));
	t_4 = (z * y) / t_3;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t_3) * z;
	elseif (t_2 <= -1.0)
		tmp = t_4;
	elseif (t_2 <= 0.9999999999965637)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+167)
		tmp = t_4;
	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[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z * y), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t$95$3), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$2, -1.0], t$95$4, If[LessEqual[t$95$2, 0.9999999999965637], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, If[LessEqual[t$95$2, 5e+167], t$95$4, t$95$1]]]]]]]]]

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))) < -inf.0

   1. Initial program 48.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 48.8

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

   5. Applied rewrites 48.8%

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

   7. Applied rewrites 80.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999997e167

   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 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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 95.5

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

   5. Applied rewrites 95.5%

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

   if -1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999996563749 or 4.9999999999999997e167 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 82.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 81.6

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

   5. Applied rewrites 81.6%

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

   if 0.999999999996563749 < (/.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 z around 0

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

   5. Applied rewrites 98.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -1:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.9999999999965637:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_2 \leq 0.9999999999965637:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_2 0.9999999999965637)
     t_1
     (if (<= t_2 2.0)
       1.0
       (if (<= t_2 5e+167) (* (/ y (* (- -1.0 x) (- x (* t z)))) z) 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.9999999999965637) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+167) {
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z;
	} 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) :: tmp
    t_1 = ((y / t) + x) / (x - (-1.0d0))
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_2 <= 0.9999999999965637d0) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_2 <= 5d+167) then
        tmp = (y / (((-1.0d0) - x) * (x - (t * z)))) * z
    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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.9999999999965637) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+167) {
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x - -1.0)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_2 <= 0.9999999999965637:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	elif t_2 <= 5e+167:
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z
	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(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= 0.9999999999965637)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+167)
		tmp = Float64(Float64(y / Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z)))) * z);
	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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_2 <= 0.9999999999965637)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+167)
		tmp = (y / ((-1.0 - x) * (x - (t * z)))) * z;
	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[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.9999999999965637], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, If[LessEqual[t$95$2, 5e+167], N[(N[(y / N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $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))) < 0.999999999996563749 or 4.9999999999999997e167 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 80.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if 0.999999999996563749 < (/.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 z around 0

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

   5. Applied rewrites 98.5%

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

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999997e167

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 85.8%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.9999999999965637:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{elif}\;t\_1 \leq 10^{+27}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{\left(-x\right) \cdot \left(x - -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 5e-6)
     (/ (+ (/ y t) x) 1.0)
     (if (<= t_1 1e+27)
       1.0
       (if (<= t_1 5e+167) (/ (* z y) (* (- x) (- x -1.0))) (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= 5e-6) {
		tmp = ((y / t) + x) / 1.0;
	} else if (t_1 <= 1e+27) {
		tmp = 1.0;
	} else if (t_1 <= 5e+167) {
		tmp = (z * y) / (-x * (x - -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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_1 <= 5d-6) then
        tmp = ((y / t) + x) / 1.0d0
    else if (t_1 <= 1d+27) then
        tmp = 1.0d0
    else if (t_1 <= 5d+167) then
        tmp = (z * y) / (-x * (x - (-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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= 5e-6) {
		tmp = ((y / t) + x) / 1.0;
	} else if (t_1 <= 1e+27) {
		tmp = 1.0;
	} else if (t_1 <= 5e+167) {
		tmp = (z * y) / (-x * (x - -1.0));
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= 5e-6:
		tmp = ((y / t) + x) / 1.0
	elif t_1 <= 1e+27:
		tmp = 1.0
	elif t_1 <= 5e+167:
		tmp = (z * y) / (-x * (x - -1.0))
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= 5e-6)
		tmp = Float64(Float64(Float64(y / t) + x) / 1.0);
	elseif (t_1 <= 1e+27)
		tmp = 1.0;
	elseif (t_1 <= 5e+167)
		tmp = Float64(Float64(z * y) / Float64(Float64(-x) * Float64(x - -1.0)));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= 5e-6)
		tmp = ((y / t) + x) / 1.0;
	elseif (t_1 <= 1e+27)
		tmp = 1.0;
	elseif (t_1 <= 5e+167)
		tmp = (z * y) / (-x * (x - -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[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-6], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+27], 1.0, If[LessEqual[t$95$1, 5e+167], N[(N[(z * y), $MachinePrecision] / N[((-x) * N[(x - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / t), $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))) < 5.00000000000000041e-6

   1. Initial program 90.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. un-div-inv N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 90.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 72.6

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 71.1%

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

   if 5.00000000000000041e-6 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1e27

   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 z around 0

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

   5. Applied rewrites 96.9%

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

   if 1e27 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999997e167

   1. Initial program 99.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.1%

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

   if 4.9999999999999997e167 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   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 x around 0

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

      1. lower-/.f64 64.4

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

   5. Applied rewrites 64.4%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 10^{+27}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{\left(-x\right) \cdot \left(x - -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{\left(x - -1\right) \cdot t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999965637:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t}}{x - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 -1e-49)
     (/ y (* (- x -1.0) t))
     (if (<= t_1 0.9999999999965637)
       (/ x (- x -1.0))
       (if (<= t_1 2.0) 1.0 (/ (/ y t) (- x -1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -1e-49) {
		tmp = y / ((x - -1.0) * t);
	} else if (t_1 <= 0.9999999999965637) {
		tmp = x / (x - -1.0);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = (y / t) / (x - -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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_1 <= (-1d-49)) then
        tmp = y / ((x - (-1.0d0)) * t)
    else if (t_1 <= 0.9999999999965637d0) then
        tmp = x / (x - (-1.0d0))
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = (y / t) / (x - (-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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -1e-49) {
		tmp = y / ((x - -1.0) * t);
	} else if (t_1 <= 0.9999999999965637) {
		tmp = x / (x - -1.0);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = (y / t) / (x - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= -1e-49:
		tmp = y / ((x - -1.0) * t)
	elif t_1 <= 0.9999999999965637:
		tmp = x / (x - -1.0)
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = (y / t) / (x - -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= -1e-49)
		tmp = Float64(y / Float64(Float64(x - -1.0) * t));
	elseif (t_1 <= 0.9999999999965637)
		tmp = Float64(x / Float64(x - -1.0));
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(Float64(y / t) / Float64(x - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= -1e-49)
		tmp = y / ((x - -1.0) * t);
	elseif (t_1 <= 0.9999999999965637)
		tmp = x / (x - -1.0);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = (y / t) / (x - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-49], N[(y / N[(N[(x - -1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999965637], N[(x / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(N[(y / t), $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))) < -9.99999999999999936e-50

   1. Initial program 83.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 66.2

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

   5. Applied rewrites 66.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 57.0%

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

   if -9.99999999999999936e-50 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999996563749

   1. Initial program 98.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. +-commutative N/A

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

      3. lower-+.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if 0.999999999996563749 < (/.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 z around 0

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

   5. Applied rewrites 98.5%

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

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

   1. Initial program 60.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 53.1

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

   5. Applied rewrites 53.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{\left(x - -1\right) \cdot t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.9999999999965637:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t}}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\left(x - -1\right) \cdot t}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.9999999999965637:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* (- x -1.0) t)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_2 -1e-49)
     t_1
     (if (<= t_2 0.9999999999965637)
       (/ x (- x -1.0))
       (if (<= t_2 2.0) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / ((x - -1.0) * t);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= -1e-49) {
		tmp = t_1;
	} else if (t_2 <= 0.9999999999965637) {
		tmp = x / (x - -1.0);
	} else if (t_2 <= 2.0) {
		tmp = 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) :: tmp
    t_1 = y / ((x - (-1.0d0)) * t)
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_2 <= (-1d-49)) then
        tmp = t_1
    else if (t_2 <= 0.9999999999965637d0) then
        tmp = x / (x - (-1.0d0))
    else if (t_2 <= 2.0d0) then
        tmp = 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 / ((x - -1.0) * t);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= -1e-49) {
		tmp = t_1;
	} else if (t_2 <= 0.9999999999965637) {
		tmp = x / (x - -1.0);
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / ((x - -1.0) * t)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_2 <= -1e-49:
		tmp = t_1
	elif t_2 <= 0.9999999999965637:
		tmp = x / (x - -1.0)
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(Float64(x - -1.0) * t))
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= -1e-49)
		tmp = t_1;
	elseif (t_2 <= 0.9999999999965637)
		tmp = Float64(x / Float64(x - -1.0));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / ((x - -1.0) * t);
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_2 <= -1e-49)
		tmp = t_1;
	elseif (t_2 <= 0.9999999999965637)
		tmp = x / (x - -1.0);
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(N[(x - -1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-49], t$95$1, If[LessEqual[t$95$2, 0.9999999999965637], N[(x / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, 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))) < -9.99999999999999936e-50 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 73.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 63.6

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

   5. Applied rewrites 63.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 55.2%

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

   if -9.99999999999999936e-50 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999996563749

   1. Initial program 98.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. +-commutative N/A

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

      3. lower-+.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if 0.999999999996563749 < (/.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 z around 0

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

   5. Applied rewrites 98.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{\left(x - -1\right) \cdot t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.9999999999965637:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(x - -1\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999965637:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 -1e-49)
     (/ y t)
     (if (<= t_1 0.9999999999965637)
       (/ x (- x -1.0))
       (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -1e-49) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999965637) {
		tmp = x / (x - -1.0);
	} 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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_1 <= (-1d-49)) then
        tmp = y / t
    else if (t_1 <= 0.9999999999965637d0) then
        tmp = x / (x - (-1.0d0))
    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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -1e-49) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999965637) {
		tmp = x / (x - -1.0);
	} 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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= -1e-49:
		tmp = y / t
	elif t_1 <= 0.9999999999965637:
		tmp = x / (x - -1.0)
	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(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= -1e-49)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999999965637)
		tmp = Float64(x / Float64(x - -1.0));
	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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= -1e-49)
		tmp = y / t;
	elseif (t_1 <= 0.9999999999965637)
		tmp = x / (x - -1.0);
	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[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-49], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999965637], N[(x / N[(x - -1.0), $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))) < -9.99999999999999936e-50 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 73.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 54.6

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

   5. Applied rewrites 54.6%

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

   if -9.99999999999999936e-50 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999996563749

   1. Initial program 98.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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. +-commutative N/A

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

      3. lower-+.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if 0.999999999996563749 < (/.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 z around 0

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

   5. Applied rewrites 98.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.9999999999965637:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 -1e-49)
     (/ y t)
     (if (<= t_1 5e-8) (* (- 1.0 x) 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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -1e-49) {
		tmp = y / t;
	} else if (t_1 <= 5e-8) {
		tmp = (1.0 - x) * 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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_1 <= (-1d-49)) then
        tmp = y / t
    else if (t_1 <= 5d-8) then
        tmp = (1.0d0 - x) * 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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -1e-49) {
		tmp = y / t;
	} else if (t_1 <= 5e-8) {
		tmp = (1.0 - x) * 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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= -1e-49:
		tmp = y / t
	elif t_1 <= 5e-8:
		tmp = (1.0 - x) * 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(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= -1e-49)
		tmp = Float64(y / t);
	elseif (t_1 <= 5e-8)
		tmp = Float64(Float64(1.0 - x) * 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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= -1e-49)
		tmp = y / t;
	elseif (t_1 <= 5e-8)
		tmp = (1.0 - x) * 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[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-49], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 5e-8], N[(N[(1.0 - x), $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))) < -9.99999999999999936e-50 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 73.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 54.6

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

   5. Applied rewrites 54.6%

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

   if -9.99999999999999936e-50 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999998e-8

   1. Initial program 97.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. un-div-inv N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 28.7

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

   7. Applied rewrites 28.7%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 53.6

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

   10. Applied rewrites 53.6%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 53.6%

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

   if 4.9999999999999998e-8 < (/.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 z around 0

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

   5. Applied rewrites 97.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_2 \leq 0.9999999999965637:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_2 0.9999999999965637) t_1 (if (<= t_2 1.2) 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.9999999999965637) {
		tmp = t_1;
	} else if (t_2 <= 1.2) {
		tmp = 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) :: tmp
    t_1 = ((y / t) + x) / (x - (-1.0d0))
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_2 <= 0.9999999999965637d0) then
        tmp = t_1
    else if (t_2 <= 1.2d0) then
        tmp = 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.9999999999965637) {
		tmp = t_1;
	} else if (t_2 <= 1.2) {
		tmp = 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_2 <= 0.9999999999965637:
		tmp = t_1
	elif t_2 <= 1.2:
		tmp = 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(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= 0.9999999999965637)
		tmp = t_1;
	elseif (t_2 <= 1.2)
		tmp = 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 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_2 <= 0.9999999999965637)
		tmp = t_1;
	elseif (t_2 <= 1.2)
		tmp = 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[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.9999999999965637], t$95$1, If[LessEqual[t$95$2, 1.2], 1.0, t$95$1]]]]

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))) < 0.999999999996563749 or 1.19999999999999996 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 82.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 71.9

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

   5. Applied rewrites 71.9%

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

   if 0.999999999996563749 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.19999999999999996

   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 z around 0

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

   5. Applied rewrites 99.2%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.9999999999965637:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 1.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t}}{x - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 5e-6)
     (/ (+ (/ y t) x) 1.0)
     (if (<= t_1 2.0) 1.0 (/ (/ y t) (- x -1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= 5e-6) {
		tmp = ((y / t) + x) / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = (y / t) / (x - -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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_1 <= 5d-6) then
        tmp = ((y / t) + x) / 1.0d0
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = (y / t) / (x - (-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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= 5e-6) {
		tmp = ((y / t) + x) / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = (y / t) / (x - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= 5e-6:
		tmp = ((y / t) + x) / 1.0
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = (y / t) / (x - -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= 5e-6)
		tmp = Float64(Float64(Float64(y / t) + x) / 1.0);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(Float64(y / t) / Float64(x - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= 5e-6)
		tmp = ((y / t) + x) / 1.0;
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = (y / t) / (x - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-6], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(N[(y / t), $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))) < 5.00000000000000041e-6

   1. Initial program 90.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. un-div-inv N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 90.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 72.6

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 71.1%

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

   if 5.00000000000000041e-6 < (/.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 z around 0

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

   5. Applied rewrites 98.3%

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

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

   1. Initial program 60.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 53.1

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

   5. Applied rewrites 53.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t}}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)) 5e-8)
   (* (- 1.0 x) x)
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 5e-8) {
		tmp = (1.0 - x) * x;
	} 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) :: tmp
    if (((x - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))) <= 5d-8) then
        tmp = (1.0d0 - x) * x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 5e-8) {
		tmp = (1.0 - x) * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 5e-8:
		tmp = (1.0 - x) * x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0)) <= 5e-8)
		tmp = Float64(Float64(1.0 - x) * x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 5e-8)
		tmp = (1.0 - x) * x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], 5e-8], N[(N[(1.0 - x), $MachinePrecision] * x), $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))) < 4.9999999999999998e-8

   1. Initial program 90.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. un-div-inv N/A

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

      11. lower-/.f64 N/A

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

   4. Applied rewrites 90.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 42.5

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

   7. Applied rewrites 42.5%

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

   8. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 35.7

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

   10. Applied rewrites 35.7%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 32.4%

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

   if 4.9999999999999998e-8 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 79.7%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.0% 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 90.8%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 52.1%

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

Developer Target 1: 99.4% 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 2024235 
(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)))