Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 95.8% → 97.8%

Time: 6.8s

Alternatives: 7

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

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 * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY)) (/ (/ x t) (- z)) (/ x (- y (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = (x / t) / -z;
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = (x / t) / -z
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 65.9%

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

      1. clear-num 65.9%

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

      2. associate-/r/ 65.9%

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

   3. Applied egg-rr 65.9%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate-/r* 65.9%

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

   6. Simplified 65.9%

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

      1. *-commutative 65.9%

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

      2. frac-2neg 65.9%

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

      3. distribute-neg-frac 65.9%

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

      4. metadata-eval 65.9%

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

      5. associate-*r/ 99.8%

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

      6. add-sqr-sqrt 37.5%

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

      7. sqrt-unprod 59.0%

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

      8. sqr-neg 59.0%

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

      9. sqrt-unprod 33.9%

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

      10. add-sqr-sqrt 65.4%

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

      11. div-inv 65.4%

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

      12. add-sqr-sqrt 33.9%

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

      13. sqrt-unprod 59.0%

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

      14. sqr-neg 59.0%

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

      15. sqrt-unprod 37.5%

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

      16. add-sqr-sqrt 100.0%

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

   8. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 z t)

   1. Initial program 98.2%

      \[\frac{x}{y - z \cdot t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]

Alternative 2: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1.2e+38)
   (* (/ x z) (/ -1.0 t))
   (if (<= (* z t) 5e-37) (/ x y) (* x (/ (/ -1.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1.2e+38) {
		tmp = (x / z) * (-1.0 / t);
	} else if ((z * t) <= 5e-37) {
		tmp = x / y;
	} else {
		tmp = x * ((-1.0 / t) / z);
	}
	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 ((z * t) <= (-1.2d+38)) then
        tmp = (x / z) * ((-1.0d0) / t)
    else if ((z * t) <= 5d-37) then
        tmp = x / y
    else
        tmp = x * (((-1.0d0) / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1.2e+38) {
		tmp = (x / z) * (-1.0 / t);
	} else if ((z * t) <= 5e-37) {
		tmp = x / y;
	} else {
		tmp = x * ((-1.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1.2e+38:
		tmp = (x / z) * (-1.0 / t)
	elif (z * t) <= 5e-37:
		tmp = x / y
	else:
		tmp = x * ((-1.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1.2e+38)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / t));
	elseif (Float64(z * t) <= 5e-37)
		tmp = Float64(x / y);
	else
		tmp = Float64(x * Float64(Float64(-1.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1.2e+38)
		tmp = (x / z) * (-1.0 / t);
	elseif ((z * t) <= 5e-37)
		tmp = x / y;
	else
		tmp = x * ((-1.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1.2e+38], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e-37], N[(x / y), $MachinePrecision], N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.20000000000000009e38

   1. Initial program 90.8%

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

      1. clear-num 90.7%

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

      2. associate-/r/ 90.6%

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

   3. Applied egg-rr 90.6%

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

   4. Taylor expanded in y around 0 82.2%

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

      1. associate-/r* 82.3%

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

   6. Simplified 82.3%

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

      1. associate-/l/ 82.2%

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

      2. associate-*l/ 82.2%

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

      3. neg-mul-1 82.2%

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

      4. *-commutative 82.2%

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

      5. expm1-log1p-u 72.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-x}{t \cdot z}\right)\right)} \]

      6. expm1-udef 44.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-x}{t \cdot z}\right)} - 1} \]

      7. neg-mul-1 44.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{-1 \cdot x}}{t \cdot z}\right)} - 1 \]

      8. *-commutative 44.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{-1 \cdot x}{\color{blue}{z \cdot t}}\right)} - 1 \]

      9. associate-*l/ 44.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-1}{z \cdot t} \cdot x}\right)} - 1 \]

      10. associate-/l/ 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\frac{-1}{t}}{z}} \cdot x\right)} - 1 \]

      11. associate-/l/ 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-1}{z \cdot t}} \cdot x\right)} - 1 \]

      12. associate-*l/ 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-1 \cdot x}{z \cdot t}}\right)} - 1 \]

      13. neg-mul-1 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{-x}}{z \cdot t}\right)} - 1 \]

      14. add-sqr-sqrt 19.4%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      15. sqrt-unprod 33.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      16. sqr-neg 33.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      17. sqrt-unprod 19.1%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      18. add-sqr-sqrt 35.7%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   8. Applied egg-rr 35.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 33.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

      2. expm1-log1p 33.9%

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

      3. associate-/l/ 35.1%

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

   10. Simplified 35.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z}} \]
   11. Step-by-step derivation

       1. add-sqr-sqrt 34.3%

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

       2. sqrt-unprod 50.7%

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

       3. clear-num 50.8%

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

       4. clear-num 50.7%

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

       5. frac-times 49.9%

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

       6. metadata-eval 49.9%

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

       7. metadata-eval 49.9%

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

       8. associate-/r/ 49.8%

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

       9. associate-/r/ 51.4%

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

       10. frac-times 52.2%

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

       11. associate-/l/ 52.3%

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

       12. associate-/l/ 52.3%

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

       13. sqrt-unprod 54.4%

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

       14. add-sqr-sqrt 88.0%

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

       15. clear-num 88.0%

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

       16. associate-/r/ 88.0%

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

       17. clear-num 88.8%

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

   12. Applied egg-rr 88.8%

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

   if -1.20000000000000009e38 < (*.f64 z t) < 4.9999999999999997e-37

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.2%

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

   if 4.9999999999999997e-37 < (*.f64 z t)

   1. Initial program 94.3%

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

      1. clear-num 94.1%

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

      2. associate-/r/ 94.2%

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

   3. Applied egg-rr 94.2%

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

   4. Taylor expanded in y around 0 82.3%

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

      1. associate-/r* 82.8%

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

   6. Simplified 82.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \end{array} \]

Alternative 3: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -1.2e+38) (not (<= (* z t) 5e-37)))
   (/ (- x) (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1.2e+38) || !((z * t) <= 5e-37)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	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 (((z * t) <= (-1.2d+38)) .or. (.not. ((z * t) <= 5d-37))) then
        tmp = -x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1.2e+38) || !((z * t) <= 5e-37)) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -1.2e+38) or not ((z * t) <= 5e-37):
		tmp = -x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -1.2e+38) || !(Float64(z * t) <= 5e-37))
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -1.2e+38) || ~(((z * t) <= 5e-37)))
		tmp = -x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -1.2e+38], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e-37]], $MachinePrecision]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.20000000000000009e38 or 4.9999999999999997e-37 < (*.f64 z t)

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

   4. Simplified 82.3%

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

   if -1.20000000000000009e38 < (*.f64 z t) < 4.9999999999999997e-37

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1.2e+38)
   (/ (/ x t) (- z))
   (if (<= (* z t) 5e-37) (/ x y) (/ (- x) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1.2e+38) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 5e-37) {
		tmp = x / y;
	} else {
		tmp = -x / (z * 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) :: tmp
    if ((z * t) <= (-1.2d+38)) then
        tmp = (x / t) / -z
    else if ((z * t) <= 5d-37) then
        tmp = x / y
    else
        tmp = -x / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1.2e+38) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 5e-37) {
		tmp = x / y;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1.2e+38:
		tmp = (x / t) / -z
	elif (z * t) <= 5e-37:
		tmp = x / y
	else:
		tmp = -x / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1.2e+38)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(z * t) <= 5e-37)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1.2e+38)
		tmp = (x / t) / -z;
	elseif ((z * t) <= 5e-37)
		tmp = x / y;
	else
		tmp = -x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1.2e+38], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e-37], N[(x / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.20000000000000009e38

   1. Initial program 90.8%

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

      1. clear-num 90.7%

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

      2. associate-/r/ 90.6%

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

   3. Applied egg-rr 90.6%

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

   4. Taylor expanded in y around 0 82.2%

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

      1. associate-/r* 82.3%

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

   6. Simplified 82.3%

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

      1. *-commutative 82.3%

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

      2. frac-2neg 82.3%

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

      3. distribute-neg-frac 82.3%

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

      4. metadata-eval 82.3%

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

      5. associate-*r/ 88.8%

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

      6. add-sqr-sqrt 39.4%

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

      7. sqrt-unprod 44.4%

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

      8. sqr-neg 44.4%

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

      9. sqrt-unprod 16.2%

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

      10. add-sqr-sqrt 35.1%

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

      11. div-inv 35.1%

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

      12. add-sqr-sqrt 16.2%

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

      13. sqrt-unprod 44.4%

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

      14. sqr-neg 44.4%

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

      15. sqrt-unprod 39.4%

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

      16. add-sqr-sqrt 88.9%

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

   8. Applied egg-rr 88.9%

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

   if -1.20000000000000009e38 < (*.f64 z t) < 4.9999999999999997e-37

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.2%

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

   if 4.9999999999999997e-37 < (*.f64 z t)

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]

Alternative 5: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1.2e+38)
   (* (/ x z) (/ -1.0 t))
   (if (<= (* z t) 5e-37) (/ x y) (/ (- x) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1.2e+38) {
		tmp = (x / z) * (-1.0 / t);
	} else if ((z * t) <= 5e-37) {
		tmp = x / y;
	} else {
		tmp = -x / (z * 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) :: tmp
    if ((z * t) <= (-1.2d+38)) then
        tmp = (x / z) * ((-1.0d0) / t)
    else if ((z * t) <= 5d-37) then
        tmp = x / y
    else
        tmp = -x / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1.2e+38) {
		tmp = (x / z) * (-1.0 / t);
	} else if ((z * t) <= 5e-37) {
		tmp = x / y;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1.2e+38:
		tmp = (x / z) * (-1.0 / t)
	elif (z * t) <= 5e-37:
		tmp = x / y
	else:
		tmp = -x / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1.2e+38)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / t));
	elseif (Float64(z * t) <= 5e-37)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1.2e+38)
		tmp = (x / z) * (-1.0 / t);
	elseif ((z * t) <= 5e-37)
		tmp = x / y;
	else
		tmp = -x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1.2e+38], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e-37], N[(x / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.20000000000000009e38

   1. Initial program 90.8%

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

      1. clear-num 90.7%

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

      2. associate-/r/ 90.6%

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

   3. Applied egg-rr 90.6%

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

   4. Taylor expanded in y around 0 82.2%

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

      1. associate-/r* 82.3%

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

   6. Simplified 82.3%

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

      1. associate-/l/ 82.2%

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

      2. associate-*l/ 82.2%

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

      3. neg-mul-1 82.2%

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

      4. *-commutative 82.2%

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

      5. expm1-log1p-u 72.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-x}{t \cdot z}\right)\right)} \]

      6. expm1-udef 44.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-x}{t \cdot z}\right)} - 1} \]

      7. neg-mul-1 44.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{-1 \cdot x}}{t \cdot z}\right)} - 1 \]

      8. *-commutative 44.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{-1 \cdot x}{\color{blue}{z \cdot t}}\right)} - 1 \]

      9. associate-*l/ 44.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-1}{z \cdot t} \cdot x}\right)} - 1 \]

      10. associate-/l/ 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\frac{-1}{t}}{z}} \cdot x\right)} - 1 \]

      11. associate-/l/ 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-1}{z \cdot t}} \cdot x\right)} - 1 \]

      12. associate-*l/ 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-1 \cdot x}{z \cdot t}}\right)} - 1 \]

      13. neg-mul-1 44.1%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{-x}}{z \cdot t}\right)} - 1 \]

      14. add-sqr-sqrt 19.4%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot t}\right)} - 1 \]

      15. sqrt-unprod 33.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot t}\right)} - 1 \]

      16. sqr-neg 33.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot t}\right)} - 1 \]

      17. sqrt-unprod 19.1%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot t}\right)} - 1 \]

      18. add-sqr-sqrt 35.7%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot t}\right)} - 1 \]

   8. Applied egg-rr 35.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 33.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot t}\right)\right)} \]

      2. expm1-log1p 33.9%

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

      3. associate-/l/ 35.1%

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

   10. Simplified 35.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z}} \]
   11. Step-by-step derivation

       1. add-sqr-sqrt 34.3%

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

       2. sqrt-unprod 50.7%

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

       3. clear-num 50.8%

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

       4. clear-num 50.7%

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

       5. frac-times 49.9%

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

       6. metadata-eval 49.9%

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

       7. metadata-eval 49.9%

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

       8. associate-/r/ 49.8%

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

       9. associate-/r/ 51.4%

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

       10. frac-times 52.2%

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

       11. associate-/l/ 52.3%

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

       12. associate-/l/ 52.3%

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

       13. sqrt-unprod 54.4%

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

       14. add-sqr-sqrt 88.0%

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

       15. clear-num 88.0%

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

       16. associate-/r/ 88.0%

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

       17. clear-num 88.8%

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

   12. Applied egg-rr 88.8%

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

   if -1.20000000000000009e38 < (*.f64 z t) < 4.9999999999999997e-37

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.2%

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

   if 4.9999999999999997e-37 < (*.f64 z t)

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]

Alternative 6: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+166} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -1e+166) (not (<= (* z t) 2e+158)))
   (/ x (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e+166) || !((z * t) <= 2e+158)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	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 (((z * t) <= (-1d+166)) .or. (.not. ((z * t) <= 2d+158))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -1e+166) || !((z * t) <= 2e+158)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -1e+166) or not ((z * t) <= 2e+158):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -1e+166) || !(Float64(z * t) <= 2e+158))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -1e+166) || ~(((z * t) <= 2e+158)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -1e+166], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+158]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.9999999999999994e165 or 1.99999999999999991e158 < (*.f64 z t)

   1. Initial program 87.6%

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

      1. clear-num 87.6%

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

      2. associate-/r/ 87.6%

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

   3. Applied egg-rr 87.6%

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

   4. Taylor expanded in y around 0 87.4%

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

      1. associate-/r* 87.9%

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

   6. Simplified 87.9%

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

      1. associate-/l/ 87.4%

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

      2. associate-*l/ 87.4%

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

      3. neg-mul-1 87.4%

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

      4. add-sqr-sqrt 41.2%

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

      5. sqrt-unprod 52.8%

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

      6. sqr-neg 52.8%

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

      7. sqrt-unprod 24.6%

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

      8. add-sqr-sqrt 50.8%

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

   8. Applied egg-rr 50.8%

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

   if -9.9999999999999994e165 < (*.f64 z t) < 1.99999999999999991e158

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 69.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+166} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 7: 54.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(x / y)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 96.2%

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

2. Taylor expanded in y around inf 54.1%

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

3. Final simplification 54.1%

   \[\leadsto \frac{x}{y} \]

Developer target: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- (/ y x) (* (/ z x) t)))))
   (if (< x -1.618195973607049e+50)
     t_1
     (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} 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) :: tmp
    t_1 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    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 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / ((y / x) - ((z / x) * t))
	tmp = 0
	if x < -1.618195973607049e+50:
		tmp = t_1
	elif x < 2.1378306434876444e+131:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(y / x) - Float64(Float64(z / x) * t)))
	tmp = 0.0
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / ((y / x) - ((z / x) * t));
	tmp = 0.0;
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[x, -1.618195973607049e+50], t$95$1, If[Less[x, 2.1378306434876444e+131], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023243 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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