Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.6% → 98.3%

Time: 7.9s

Alternatives: 11

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+297}\right):\\ \;\;\;\;\left(t + z\right) \cdot \left(\frac{x}{t + z} \cdot \frac{y - z}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+297)))
     (* (+ t z) (* (/ x (+ t z)) (/ (- y z) (- t z))))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+297)) {
		tmp = (t + z) * ((x / (t + z)) * ((y - z) / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+297)) {
		tmp = (t + z) * ((x / (t + z)) * ((y - z) / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+297):
		tmp = (t + z) * ((x / (t + z)) * ((y - z) / (t - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+297))
		tmp = Float64(Float64(t + z) * Float64(Float64(x / Float64(t + z)) * Float64(Float64(y - z) / Float64(t - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+297)))
		tmp = (t + z) * ((x / (t + z)) * ((y - z) / (t - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+297]], $MachinePrecision]], N[(N[(t + z), $MachinePrecision] * N[(N[(x / N[(t + z), $MachinePrecision]), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -inf.0 or 2e297 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 35.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. difference-of-squares N/A

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

      10. lift--.f64 N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 2e297

   1. Initial program 98.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+297}\right):\\ \;\;\;\;\left(t + z\right) \cdot \left(\frac{x}{t + z} \cdot \frac{y - z}{t - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ t_2 := \frac{x}{t - z} \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-288}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;t\_1 \leq 50000000000:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))) (t_2 (* (/ x (- t z)) y)))
   (if (<= t_1 -5e+15)
     t_2
     (if (<= t_1 5e-288)
       (/ (* (- y z) x) t)
       (if (<= t_1 50000000000.0)
         (- x (/ (* y x) z))
         (if (<= t_1 2e+58) t_2 (* (- z y) (/ x z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double t_2 = (x / (t - z)) * y;
	double tmp;
	if (t_1 <= -5e+15) {
		tmp = t_2;
	} else if (t_1 <= 5e-288) {
		tmp = ((y - z) * x) / t;
	} else if (t_1 <= 50000000000.0) {
		tmp = x - ((y * x) / z);
	} else if (t_1 <= 2e+58) {
		tmp = t_2;
	} else {
		tmp = (z - y) * (x / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (y - z)) / (t - z)
    t_2 = (x / (t - z)) * y
    if (t_1 <= (-5d+15)) then
        tmp = t_2
    else if (t_1 <= 5d-288) then
        tmp = ((y - z) * x) / t
    else if (t_1 <= 50000000000.0d0) then
        tmp = x - ((y * x) / z)
    else if (t_1 <= 2d+58) then
        tmp = t_2
    else
        tmp = (z - y) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double t_2 = (x / (t - z)) * y;
	double tmp;
	if (t_1 <= -5e+15) {
		tmp = t_2;
	} else if (t_1 <= 5e-288) {
		tmp = ((y - z) * x) / t;
	} else if (t_1 <= 50000000000.0) {
		tmp = x - ((y * x) / z);
	} else if (t_1 <= 2e+58) {
		tmp = t_2;
	} else {
		tmp = (z - y) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	t_2 = (x / (t - z)) * y
	tmp = 0
	if t_1 <= -5e+15:
		tmp = t_2
	elif t_1 <= 5e-288:
		tmp = ((y - z) * x) / t
	elif t_1 <= 50000000000.0:
		tmp = x - ((y * x) / z)
	elif t_1 <= 2e+58:
		tmp = t_2
	else:
		tmp = (z - y) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	t_2 = Float64(Float64(x / Float64(t - z)) * y)
	tmp = 0.0
	if (t_1 <= -5e+15)
		tmp = t_2;
	elseif (t_1 <= 5e-288)
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	elseif (t_1 <= 50000000000.0)
		tmp = Float64(x - Float64(Float64(y * x) / z));
	elseif (t_1 <= 2e+58)
		tmp = t_2;
	else
		tmp = Float64(Float64(z - y) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	t_2 = (x / (t - z)) * y;
	tmp = 0.0;
	if (t_1 <= -5e+15)
		tmp = t_2;
	elseif (t_1 <= 5e-288)
		tmp = ((y - z) * x) / t;
	elseif (t_1 <= 50000000000.0)
		tmp = x - ((y * x) / z);
	elseif (t_1 <= 2e+58)
		tmp = t_2;
	else
		tmp = (z - y) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+15], t$95$2, If[LessEqual[t$95$1, 5e-288], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 50000000000.0], N[(x - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+58], t$95$2, N[(N[(z - y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -5e15 or 5e10 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.99999999999999989e58

   1. Initial program 78.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 60.1

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

   5. Applied rewrites 60.1%

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

   if -5e15 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.00000000000000011e-288

   1. Initial program 96.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. difference-of-squares N/A

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

      10. lift--.f64 N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-/.f64 67.6

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

   4. Applied rewrites 67.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 65.8

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

   7. Applied rewrites 65.8%

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

   if 5.00000000000000011e-288 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5e10

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.6%

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

   if 1.99999999999999989e58 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 67.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 57.4

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

   5. Applied rewrites 57.4%

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

   7. Applied rewrites 59.6%

      \[\leadsto \left(z - y\right) \cdot \color{blue}{\frac{x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{-288}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 50000000000:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (<= t_1 -5e+118)
     (* (/ x (- t z)) y)
     (if (<= t_1 2e+297) t_1 (* (/ (- z y) z) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -5e+118) {
		tmp = (x / (t - z)) * y;
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = ((z - y) / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (y - z)) / (t - z)
    if (t_1 <= (-5d+118)) then
        tmp = (x / (t - z)) * y
    else if (t_1 <= 2d+297) then
        tmp = t_1
    else
        tmp = ((z - y) / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -5e+118) {
		tmp = (x / (t - z)) * y;
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = ((z - y) / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= -5e+118:
		tmp = (x / (t - z)) * y
	elif t_1 <= 2e+297:
		tmp = t_1
	else:
		tmp = ((z - y) / z) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -5e+118)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= -5e+118)
		tmp = (x / (t - z)) * y;
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = ((z - y) / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+118], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+297], t$95$1, N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -4.99999999999999972e118

   1. Initial program 63.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 60.5

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

   5. Applied rewrites 60.5%

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

   if -4.99999999999999972e118 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 2e297

   1. Initial program 98.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   if 2e297 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 27.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-38}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-25}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+77)
   (* 1.0 x)
   (if (<= z -5.8e-38)
     (* (- x) (/ z t))
     (if (<= z 9e-25) (/ (* y x) t) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+77) {
		tmp = 1.0 * x;
	} else if (z <= -5.8e-38) {
		tmp = -x * (z / t);
	} else if (z <= 9e-25) {
		tmp = (y * x) / t;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-1.05d+77)) then
        tmp = 1.0d0 * x
    else if (z <= (-5.8d-38)) then
        tmp = -x * (z / t)
    else if (z <= 9d-25) then
        tmp = (y * x) / t
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+77) {
		tmp = 1.0 * x;
	} else if (z <= -5.8e-38) {
		tmp = -x * (z / t);
	} else if (z <= 9e-25) {
		tmp = (y * x) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+77:
		tmp = 1.0 * x
	elif z <= -5.8e-38:
		tmp = -x * (z / t)
	elif z <= 9e-25:
		tmp = (y * x) / t
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+77)
		tmp = Float64(1.0 * x);
	elseif (z <= -5.8e-38)
		tmp = Float64(Float64(-x) * Float64(z / t));
	elseif (z <= 9e-25)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+77)
		tmp = 1.0 * x;
	elseif (z <= -5.8e-38)
		tmp = -x * (z / t);
	elseif (z <= 9e-25)
		tmp = (y * x) / t;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+77], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, -5.8e-38], N[((-x) * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-25], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0499999999999999e77 or 9.0000000000000002e-25 < z

   1. Initial program 77.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 80.3

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 63.7%

      \[\leadsto 1 \cdot x \]

   if -1.0499999999999999e77 < z < -5.79999999999999988e-38

   1. Initial program 95.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. difference-of-squares N/A

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

      10. lift--.f64 N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-/.f64 92.2

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

   4. Applied rewrites 92.2%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 54.4

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

   7. Applied rewrites 54.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 55.1%

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

   if -5.79999999999999988e-38 < z < 9.0000000000000002e-25

   1. Initial program 93.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-38}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-25}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -44000000000 \lor \neg \left(t \leq 1.05 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -44000000000.0) (not (<= t 1.05e+38)))
   (* (/ (- y z) t) x)
   (* (/ (- z y) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -44000000000.0) || !(t <= 1.05e+38)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = ((z - y) / z) * x;
	}
	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 <= (-44000000000.0d0)) .or. (.not. (t <= 1.05d+38))) then
        tmp = ((y - z) / t) * x
    else
        tmp = ((z - y) / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -44000000000.0) || !(t <= 1.05e+38)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = ((z - y) / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -44000000000.0) or not (t <= 1.05e+38):
		tmp = ((y - z) / t) * x
	else:
		tmp = ((z - y) / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -44000000000.0) || !(t <= 1.05e+38))
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -44000000000.0) || ~((t <= 1.05e+38)))
		tmp = ((y - z) / t) * x;
	else
		tmp = ((z - y) / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -44000000000.0], N[Not[LessEqual[t, 1.05e+38]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e10 or 1.05e38 < t

   1. Initial program 88.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -4.4e10 < t < 1.05e38

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -44000000000 \lor \neg \left(t \leq 1.05 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -44000000000 \lor \neg \left(t \leq 2.4 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -44000000000.0) (not (<= t 2.4e+29)))
   (* (/ (- y z) t) x)
   (- x (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -44000000000.0) || !(t <= 2.4e+29)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = x - ((y * x) / 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 ((t <= (-44000000000.0d0)) .or. (.not. (t <= 2.4d+29))) then
        tmp = ((y - z) / t) * x
    else
        tmp = x - ((y * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -44000000000.0) || !(t <= 2.4e+29)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = x - ((y * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -44000000000.0) or not (t <= 2.4e+29):
		tmp = ((y - z) / t) * x
	else:
		tmp = x - ((y * x) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -44000000000.0) || !(t <= 2.4e+29))
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = Float64(x - Float64(Float64(y * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -44000000000.0) || ~((t <= 2.4e+29)))
		tmp = ((y - z) / t) * x;
	else
		tmp = x - ((y * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -44000000000.0], N[Not[LessEqual[t, 2.4e+29]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], N[(x - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e10 or 2.4000000000000001e29 < t

   1. Initial program 88.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -4.4e10 < t < 2.4000000000000001e29

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -44000000000 \lor \neg \left(t \leq 2.4 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -44000000000 \lor \neg \left(t \leq 9 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -44000000000.0) (not (<= t 9e+37)))
   (/ (* (- y z) x) t)
   (- x (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -44000000000.0) || !(t <= 9e+37)) {
		tmp = ((y - z) * x) / t;
	} else {
		tmp = x - ((y * x) / 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 ((t <= (-44000000000.0d0)) .or. (.not. (t <= 9d+37))) then
        tmp = ((y - z) * x) / t
    else
        tmp = x - ((y * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -44000000000.0) || !(t <= 9e+37)) {
		tmp = ((y - z) * x) / t;
	} else {
		tmp = x - ((y * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -44000000000.0) or not (t <= 9e+37):
		tmp = ((y - z) * x) / t
	else:
		tmp = x - ((y * x) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -44000000000.0) || !(t <= 9e+37))
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	else
		tmp = Float64(x - Float64(Float64(y * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -44000000000.0) || ~((t <= 9e+37)))
		tmp = ((y - z) * x) / t;
	else
		tmp = x - ((y * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -44000000000.0], N[Not[LessEqual[t, 9e+37]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision], N[(x - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e10 or 8.99999999999999923e37 < t

   1. Initial program 88.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. difference-of-squares N/A

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

      10. lift--.f64 N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-/.f64 69.0

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

   4. Applied rewrites 69.0%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 79.8

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

   7. Applied rewrites 79.8%

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

   if -4.4e10 < t < 8.99999999999999923e37

   1. Initial program 85.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -44000000000 \lor \neg \left(t \leq 9 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+77} \lor \neg \left(z \leq 3.15 \cdot 10^{+40}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.25e+77) (not (<= z 3.15e+40)))
   (* 1.0 x)
   (/ (* (- y z) x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e+77) || !(z <= 3.15e+40)) {
		tmp = 1.0 * x;
	} else {
		tmp = ((y - z) * x) / 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 <= (-2.25d+77)) .or. (.not. (z <= 3.15d+40))) then
        tmp = 1.0d0 * x
    else
        tmp = ((y - z) * x) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e+77) || !(z <= 3.15e+40)) {
		tmp = 1.0 * x;
	} else {
		tmp = ((y - z) * x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.25e+77) or not (z <= 3.15e+40):
		tmp = 1.0 * x
	else:
		tmp = ((y - z) * x) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.25e+77) || !(z <= 3.15e+40))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.25e+77) || ~((z <= 3.15e+40)))
		tmp = 1.0 * x;
	else
		tmp = ((y - z) * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.25e+77], N[Not[LessEqual[z, 3.15e+40]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25000000000000012e77 or 3.15000000000000003e40 < z

   1. Initial program 75.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 84.5

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 68.5%

      \[\leadsto 1 \cdot x \]

   if -2.25000000000000012e77 < z < 3.15000000000000003e40

   1. Initial program 93.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. difference-of-squares N/A

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

      10. lift--.f64 N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-/.f64 80.9

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

   4. Applied rewrites 80.9%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 70.4

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

   7. Applied rewrites 70.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+77} \lor \neg \left(z \leq 3.15 \cdot 10^{+40}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00135 \lor \neg \left(z \leq 9 \cdot 10^{-25}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00135) (not (<= z 9e-25))) (* 1.0 x) (/ (* y x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00135) || !(z <= 9e-25)) {
		tmp = 1.0 * x;
	} else {
		tmp = (y * x) / 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 <= (-0.00135d0)) .or. (.not. (z <= 9d-25))) then
        tmp = 1.0d0 * x
    else
        tmp = (y * x) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00135) || !(z <= 9e-25)) {
		tmp = 1.0 * x;
	} else {
		tmp = (y * x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00135) or not (z <= 9e-25):
		tmp = 1.0 * x
	else:
		tmp = (y * x) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00135) || !(z <= 9e-25))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(y * x) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00135) || ~((z <= 9e-25)))
		tmp = 1.0 * x;
	else
		tmp = (y * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00135], N[Not[LessEqual[z, 9e-25]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0013500000000000001 or 9.0000000000000002e-25 < z

   1. Initial program 79.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 76.7

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 59.7%

      \[\leadsto 1 \cdot x \]

   if -0.0013500000000000001 < z < 9.0000000000000002e-25

   1. Initial program 93.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 68.8

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

   5. Applied rewrites 68.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00135 \lor \neg \left(z \leq 9 \cdot 10^{-25}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00135 \lor \neg \left(z \leq 270000\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00135) (not (<= z 270000.0))) (* 1.0 x) (* x (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00135) || !(z <= 270000.0)) {
		tmp = 1.0 * x;
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.00135d0)) .or. (.not. (z <= 270000.0d0))) then
        tmp = 1.0d0 * x
    else
        tmp = x * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00135) || !(z <= 270000.0)) {
		tmp = 1.0 * x;
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00135) or not (z <= 270000.0):
		tmp = 1.0 * x
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00135) || !(z <= 270000.0))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00135) || ~((z <= 270000.0)))
		tmp = 1.0 * x;
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00135], N[Not[LessEqual[z, 270000.0]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0013500000000000001 or 2.7e5 < z

   1. Initial program 79.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

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

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lft-identity N/A

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

      19. lower--.f64 77.7

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 61.3%

      \[\leadsto 1 \cdot x \]

   if -0.0013500000000000001 < z < 2.7e5

   1. Initial program 93.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   7. Applied rewrites 66.9%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00135 \lor \neg \left(z \leq 270000\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.4% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

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 * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 86.8%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Add Preprocessing

3. Taylor expanded in t around 0

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

   1. mul-1-neg N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

   5. lower-*.f64 N/A

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

   6. distribute-neg-frac N/A

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

   7. lower-/.f64 N/A

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

   8. *-lft-identity N/A

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

   9. metadata-eval N/A

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

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

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. mul-1-neg N/A

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

   14. remove-double-neg N/A

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

   15. mul-1-neg N/A

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

   16. metadata-eval N/A

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

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

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

   18. *-lft-identity N/A

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

   19. lower--.f64 50.4

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

5. Applied rewrites 50.4%

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

6. Taylor expanded in y around 0

   \[\leadsto 1 \cdot x \]
7. Step-by-step derivation

8. Applied rewrites 34.0%

   \[\leadsto 1 \cdot x \]

9. Final simplification 34.0%

   \[\leadsto 1 \cdot x \]
10. Add Preprocessing

Developer Target 1: 96.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024320 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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