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

Percentage Accurate: 89.9% → 96.0%

Time: 12.6s

Alternatives: 11

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: 89.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+181}:\\ \;\;\;\;\frac{z}{t\_1} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+208}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -2e+181)
     (* (/ z t_1) (/ y (+ x 1.0)))
     (if (<= t_2 2e+208) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+181) {
		tmp = (z / t_1) * (y / (x + 1.0));
	} else if (t_2 <= 2e+208) {
		tmp = t_2;
	} else {
		tmp = (x + (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) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-2d+181)) then
        tmp = (z / t_1) * (y / (x + 1.0d0))
    else if (t_2 <= 2d+208) then
        tmp = t_2
    else
        tmp = (x + (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 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+181) {
		tmp = (z / t_1) * (y / (x + 1.0));
	} else if (t_2 <= 2e+208) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -2e+181:
		tmp = (z / t_1) * (y / (x + 1.0))
	elif t_2 <= 2e+208:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -2e+181)
		tmp = Float64(Float64(z / t_1) * Float64(y / Float64(x + 1.0)));
	elseif (t_2 <= 2e+208)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -2e+181)
		tmp = (z / t_1) * (y / (x + 1.0));
	elseif (t_2 <= 2e+208)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+181], N[(N[(z / t$95$1), $MachinePrecision] * N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+208], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $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))) < -1.9999999999999998e181

   1. Initial program 39.9%

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

      1. *-commutative 39.9%

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

   3. Simplified 39.9%

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

   5. Taylor expanded in y around inf 39.3%

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

      1. *-commutative 39.3%

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

      2. +-commutative 39.3%

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

      3. *-commutative 39.3%

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

      4. times-frac 81.5%

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

   7. Applied egg-rr 81.5%

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

   if -1.9999999999999998e181 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2e208

   1. Initial program 99.4%

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

   if 2e208 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 42.4%

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

      1. *-commutative 42.4%

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

   3. Simplified 42.4%

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

   5. Taylor expanded in z around inf 83.1%

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

      1. +-commutative 83.1%

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

      2. +-commutative 83.1%

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

   7. Simplified 83.1%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{+181}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+208}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-49} \lor \neg \left(t \leq 5.9 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \left(\frac{y}{\frac{x}{z}} - x\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.45e-49) (not (<= t 5.9e-92)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- 1.0 (- (/ y (/ x z)) x)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-49) || !(t <= 5.9e-92)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 - ((y / (x / z)) - x)) / (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) :: tmp
    if ((t <= (-1.45d-49)) .or. (.not. (t <= 5.9d-92))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (1.0d0 - ((y / (x / z)) - x)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-49) || !(t <= 5.9e-92)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 - ((y / (x / z)) - x)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.45e-49) or not (t <= 5.9e-92):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (1.0 - ((y / (x / z)) - x)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.45e-49) || !(t <= 5.9e-92))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 - Float64(Float64(y / Float64(x / z)) - x)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.45e-49) || ~((t <= 5.9e-92)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (1.0 - ((y / (x / z)) - x)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.45e-49], N[Not[LessEqual[t, 5.9e-92]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e-49 or 5.9e-92 < t

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. +-commutative 85.8%

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

   7. Simplified 85.8%

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

   if -1.45e-49 < t < 5.9e-92

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. unsub-neg 76.1%

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

      3. associate-/l* 80.9%

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

      4. +-commutative 80.9%

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

   7. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. un-div-inv 80.9%

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

   9. Applied egg-rr 80.9%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-49} \lor \neg \left(t \leq 5.9 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \left(\frac{y}{\frac{x}{z}} - x\right)}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-50} \lor \neg \left(t \leq 1.48 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e-50) (not (<= t 1.48e-92)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ 1.0 (- x (* y (/ z x)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-50) || !(t <= 1.48e-92)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y * (z / x)))) / (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) :: tmp
    if ((t <= (-8.5d-50)) .or. (.not. (t <= 1.48d-92))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (1.0d0 + (x - (y * (z / x)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-50) || !(t <= 1.48e-92)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y * (z / x)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e-50) or not (t <= 1.48e-92):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (1.0 + (x - (y * (z / x)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e-50) || !(t <= 1.48e-92))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y * Float64(z / x)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e-50) || ~((t <= 1.48e-92)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (1.0 + (x - (y * (z / x)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e-50], N[Not[LessEqual[t, 1.48e-92]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000012e-50 or 1.48000000000000001e-92 < t

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. +-commutative 85.8%

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

   7. Simplified 85.8%

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

   if -8.50000000000000012e-50 < t < 1.48000000000000001e-92

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. unsub-neg 76.1%

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

      3. associate-/l* 80.9%

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

      4. +-commutative 80.9%

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

   7. Simplified 80.9%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-50} \lor \neg \left(t \leq 1.48 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-66}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e-35)
   (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))
   (if (<= x 1.65e-66)
     (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
     (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-35) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if (x <= 1.65e-66) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (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) :: tmp
    if (x <= (-8.5d-35)) then
        tmp = (1.0d0 + (x - (y / (x / z)))) / (x + 1.0d0)
    else if (x <= 1.65d-66) then
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 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 <= -8.5e-35) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if (x <= 1.65e-66) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e-35:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	elif x <= 1.65e-66:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e-35)
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	elseif (x <= 1.65e-66)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e-35)
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	elseif (x <= 1.65e-66)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e-35], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-66], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000001e-35

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around 0 80.1%

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

      1. mul-1-neg 80.1%

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

      2. unsub-neg 80.1%

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

      3. associate-/l* 88.6%

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

      4. +-commutative 88.6%

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

   7. Simplified 88.6%

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

      1. clear-num 88.6%

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

      2. un-div-inv 88.6%

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

   9. Applied egg-rr 88.6%

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

   if -8.5000000000000001e-35 < x < 1.6499999999999999e-66

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in t around -inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

      3. sub-neg 78.7%

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

      4. mul-1-neg 78.7%

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

      5. remove-double-neg 78.7%

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

      6. +-commutative 78.7%

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

      7. mul-1-neg 78.7%

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

      8. unsub-neg 78.7%

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

   7. Simplified 78.7%

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

   if 1.6499999999999999e-66 < x

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 91.5%

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

      1. +-commutative 91.5%

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

   7. Simplified 91.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-66}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-211}:\\ \;\;\;\;\frac{y}{t \cdot \left(\left(-x\right) - -1\right)}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.8e-74)
   1.0
   (if (<= x 3.9e-211)
     (/ y (* t (- (- x) -1.0)))
     (if (<= x 4e-65) (- x (/ x (* z t))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e-74) {
		tmp = 1.0;
	} else if (x <= 3.9e-211) {
		tmp = y / (t * (-x - -1.0));
	} else if (x <= 4e-65) {
		tmp = x - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.8d-74)) then
        tmp = 1.0d0
    else if (x <= 3.9d-211) then
        tmp = y / (t * (-x - (-1.0d0)))
    else if (x <= 4d-65) then
        tmp = x - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e-74) {
		tmp = 1.0;
	} else if (x <= 3.9e-211) {
		tmp = y / (t * (-x - -1.0));
	} else if (x <= 4e-65) {
		tmp = x - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.8e-74:
		tmp = 1.0
	elif x <= 3.9e-211:
		tmp = y / (t * (-x - -1.0))
	elif x <= 4e-65:
		tmp = x - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.8e-74)
		tmp = 1.0;
	elseif (x <= 3.9e-211)
		tmp = Float64(y / Float64(t * Float64(Float64(-x) - -1.0)));
	elseif (x <= 4e-65)
		tmp = Float64(x - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.8e-74)
		tmp = 1.0;
	elseif (x <= 3.9e-211)
		tmp = y / (t * (-x - -1.0));
	elseif (x <= 4e-65)
		tmp = x - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.8e-74], 1.0, If[LessEqual[x, 3.9e-211], N[(y / N[(t * N[((-x) - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-65], N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8000000000000001e-74 or 3.99999999999999969e-65 < x

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 82.2%

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

   if -6.8000000000000001e-74 < x < 3.8999999999999996e-211

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 76.2%

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

      1. +-commutative 76.2%

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

      2. +-commutative 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in y around inf 63.0%

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

      1. +-commutative 63.0%

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

   10. Simplified 63.0%

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

       1. frac-2neg 63.0%

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

       2. div-inv 62.8%

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

       3. distribute-rgt-neg-in 62.8%

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

       4. distribute-neg-in 62.8%

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

       5. add-sqr-sqrt 37.8%

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

       6. sqrt-unprod 62.8%

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

       7. sqr-neg 62.8%

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

       8. sqrt-unprod 25.0%

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

       9. add-sqr-sqrt 62.8%

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

       10. metadata-eval 62.8%

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

   12. Applied egg-rr 62.8%

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

       1. distribute-lft-neg-out 62.8%

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

       2. associate-*r/ 63.0%

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

       3. *-rgt-identity 63.0%

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

       4. distribute-neg-frac2 63.0%

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

       5. *-commutative 63.0%

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

       6. distribute-rgt-neg-in 63.0%

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

   14. Simplified 63.0%

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

   if 3.8999999999999996e-211 < x < 3.99999999999999969e-65

   1. Initial program 98.8%

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

      1. *-commutative 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around -inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. unsub-neg 68.4%

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

      3. sub-neg 68.4%

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

      4. mul-1-neg 68.4%

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

      5. remove-double-neg 68.4%

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

      6. +-commutative 68.4%

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

      7. mul-1-neg 68.4%

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

      8. unsub-neg 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in x around inf 49.1%

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

   9. Taylor expanded in x around 0 48.9%

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

       1. sub-neg 48.9%

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

       2. distribute-lft-in 48.9%

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

       3. *-rgt-identity 48.9%

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

       4. distribute-rgt-neg-in 48.9%

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

       5. *-commutative 48.9%

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

       6. associate-*r/ 49.2%

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

       7. associate-*l/ 49.2%

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

       8. *-rgt-identity 49.2%

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

       9. unsub-neg 49.2%

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

   11. Simplified 49.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-211}:\\ \;\;\;\;\frac{y}{t \cdot \left(\left(-x\right) - -1\right)}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{-211}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e-74)
   1.0
   (if (<= x 7.1e-211) (/ y t) (if (<= x 1.62e-63) (- x (/ x (* z t))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-74) {
		tmp = 1.0;
	} else if (x <= 7.1e-211) {
		tmp = y / t;
	} else if (x <= 1.62e-63) {
		tmp = x - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7.6d-74)) then
        tmp = 1.0d0
    else if (x <= 7.1d-211) then
        tmp = y / t
    else if (x <= 1.62d-63) then
        tmp = x - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-74) {
		tmp = 1.0;
	} else if (x <= 7.1e-211) {
		tmp = y / t;
	} else if (x <= 1.62e-63) {
		tmp = x - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.6e-74:
		tmp = 1.0
	elif x <= 7.1e-211:
		tmp = y / t
	elif x <= 1.62e-63:
		tmp = x - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e-74)
		tmp = 1.0;
	elseif (x <= 7.1e-211)
		tmp = Float64(y / t);
	elseif (x <= 1.62e-63)
		tmp = Float64(x - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.6e-74)
		tmp = 1.0;
	elseif (x <= 7.1e-211)
		tmp = y / t;
	elseif (x <= 1.62e-63)
		tmp = x - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e-74], 1.0, If[LessEqual[x, 7.1e-211], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.62e-63], N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5999999999999993e-74 or 1.6200000000000001e-63 < x

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 82.2%

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

   if -7.5999999999999993e-74 < x < 7.09999999999999987e-211

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in x around 0 63.0%

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

   if 7.09999999999999987e-211 < x < 1.6200000000000001e-63

   1. Initial program 98.8%

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

      1. *-commutative 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around -inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. unsub-neg 68.4%

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

      3. sub-neg 68.4%

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

      4. mul-1-neg 68.4%

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

      5. remove-double-neg 68.4%

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

      6. +-commutative 68.4%

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

      7. mul-1-neg 68.4%

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

      8. unsub-neg 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in x around inf 49.1%

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

   9. Taylor expanded in x around 0 48.9%

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

       1. sub-neg 48.9%

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

       2. distribute-lft-in 48.9%

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

       3. *-rgt-identity 48.9%

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

       4. distribute-rgt-neg-in 48.9%

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

       5. *-commutative 48.9%

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

       6. associate-*r/ 49.2%

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

       7. associate-*l/ 49.2%

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

       8. *-rgt-identity 49.2%

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

       9. unsub-neg 49.2%

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

   11. Simplified 49.2%

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

Alternative 7: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-49} \lor \neg \left(t \leq 1.42 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x \cdot \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e-49) (not (<= t 1.42e-91)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* y (/ z (* x (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-49) || !(t <= 1.42e-91)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / (x * (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) :: tmp
    if ((t <= (-8.5d-49)) .or. (.not. (t <= 1.42d-91))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y * (z / (x * (x + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-49) || !(t <= 1.42e-91)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y * (z / (x * (x + 1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e-49) or not (t <= 1.42e-91):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (y * (z / (x * (x + 1.0))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e-49) || !(t <= 1.42e-91))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y * Float64(z / Float64(x * Float64(x + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e-49) || ~((t <= 1.42e-91)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (y * (z / (x * (x + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e-49], N[Not[LessEqual[t, 1.42e-91]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(z / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000069e-49 or 1.4199999999999999e-91 < t

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. +-commutative 85.8%

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

   7. Simplified 85.8%

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

   if -8.50000000000000069e-49 < t < 1.4199999999999999e-91

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. unsub-neg 76.1%

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

      3. associate-/l* 80.9%

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

      4. +-commutative 80.9%

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

   7. Simplified 80.9%

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

   8. Taylor expanded in y around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. sub-neg 76.0%

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

      3. associate-/l* 78.9%

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

      4. +-commutative 78.9%

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

   10. Simplified 78.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-49} \lor \neg \left(t \leq 1.42 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \frac{z}{x \cdot \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{-211}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e-73)
   1.0
   (if (<= x 7.1e-211) (/ y t) (if (<= x 1.02e-75) (/ x (+ x 1.0)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-73) {
		tmp = 1.0;
	} else if (x <= 7.1e-211) {
		tmp = y / t;
	} else if (x <= 1.02e-75) {
		tmp = x / (x + 1.0);
	} 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 <= (-1.35d-73)) then
        tmp = 1.0d0
    else if (x <= 7.1d-211) then
        tmp = y / t
    else if (x <= 1.02d-75) then
        tmp = x / (x + 1.0d0)
    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 <= -1.35e-73) {
		tmp = 1.0;
	} else if (x <= 7.1e-211) {
		tmp = y / t;
	} else if (x <= 1.02e-75) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e-73:
		tmp = 1.0
	elif x <= 7.1e-211:
		tmp = y / t
	elif x <= 1.02e-75:
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e-73)
		tmp = 1.0;
	elseif (x <= 7.1e-211)
		tmp = Float64(y / t);
	elseif (x <= 1.02e-75)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.35e-73)
		tmp = 1.0;
	elseif (x <= 7.1e-211)
		tmp = y / t;
	elseif (x <= 1.02e-75)
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e-73], 1.0, If[LessEqual[x, 7.1e-211], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.02e-75], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.34999999999999997e-73 or 1.01999999999999997e-75 < x

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around inf 81.2%

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

   if -1.34999999999999997e-73 < x < 7.09999999999999987e-211

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in x around 0 63.0%

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

   if 7.09999999999999987e-211 < x < 1.01999999999999997e-75

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 45.1%

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

      1. +-commutative 45.1%

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

   7. Simplified 45.1%

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

Alternative 9: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00125:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.00125) 1.0 (if (<= x 9.6e-51) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.00125) {
		tmp = 1.0;
	} else if (x <= 9.6e-51) {
		tmp = (x + (y / t)) / (x + 1.0);
	} 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 <= (-0.00125d0)) then
        tmp = 1.0d0
    else if (x <= 9.6d-51) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    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 <= -0.00125) {
		tmp = 1.0;
	} else if (x <= 9.6e-51) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.00125:
		tmp = 1.0
	elif x <= 9.6e-51:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.00125)
		tmp = 1.0;
	elseif (x <= 9.6e-51)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.00125)
		tmp = 1.0;
	elseif (x <= 9.6e-51)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.00125], 1.0, If[LessEqual[x, 9.6e-51], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00125000000000000003 or 9.6000000000000001e-51 < x

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around inf 88.2%

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

   if -0.00125000000000000003 < x < 9.6000000000000001e-51

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. +-commutative 67.6%

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

   7. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{\frac{y}{t} + x}{x + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00125:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.32e-73) 1.0 (if (<= x 4.5e-84) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.32e-73) {
		tmp = 1.0;
	} else if (x <= 4.5e-84) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.32d-73)) then
        tmp = 1.0d0
    else if (x <= 4.5d-84) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.32e-73) {
		tmp = 1.0;
	} else if (x <= 4.5e-84) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.32e-73:
		tmp = 1.0
	elif x <= 4.5e-84:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.32e-73)
		tmp = 1.0;
	elseif (x <= 4.5e-84)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.32e-73)
		tmp = 1.0;
	elseif (x <= 4.5e-84)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.32e-73], 1.0, If[LessEqual[x, 4.5e-84], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.31999999999999998e-73 or 4.50000000000000016e-84 < x

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -1.31999999999999998e-73 < x < 4.50000000000000016e-84

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in x around 0 54.2%

      \[\leadsto \color{blue}{\frac{y}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 53.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. *-commutative 91.9%

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

3. Simplified 91.9%

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

5. Taylor expanded in x around inf 57.5%

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

Developer Target 1: 99.5% accurate, 0.8× 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 2024123 
(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)))