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

Percentage Accurate: 84.0% → 96.8%

Time: 10.1s

Alternatives: 14

Speedup: 1.0×

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: 84.0% 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: 96.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{-10}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{\frac{z - t}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1e-10) (/ (* x_m (- y z)) (- t z)) (/ (- z y) (/ (- z t) x_m)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1e-10) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (z - y) / ((z - t) / x_m);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 1d-10) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (z - y) / ((z - t) / x_m)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1e-10) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (z - y) / ((z - t) / x_m);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 1e-10:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (z - y) / ((z - t) / x_m)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1e-10)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(z - y) / Float64(Float64(z - t) / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 1e-10)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (z - y) / ((z - t) / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1e-10], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000004e-10

   1. Initial program 89.2%

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

   if 1.00000000000000004e-10 < x

   1. Initial program 72.7%

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

      1. remove-double-neg 72.7%

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

      2. distribute-lft-neg-out 72.7%

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

      3. distribute-neg-frac 72.7%

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

      4. distribute-neg-frac2 72.7%

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

      5. distribute-lft-neg-out 72.7%

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

      6. distribute-rgt-neg-in 72.7%

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

      7. sub-neg 72.7%

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

      8. distribute-neg-in 72.7%

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

      9. remove-double-neg 72.7%

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

      10. +-commutative 72.7%

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

      11. sub-neg 72.7%

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

      12. sub-neg 72.7%

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

      13. distribute-neg-in 72.7%

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

      14. remove-double-neg 72.7%

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

      15. +-commutative 72.7%

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

      16. sub-neg 72.7%

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

   3. Simplified 72.7%

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

      1. *-commutative 72.7%

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

      2. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   8. Applied egg-rr 99.7%

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

4. Final simplification 92.0%

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

Alternative 2: 74.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y}{t - z}\\ t_2 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -0.32:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-273}:\\ \;\;\;\;\frac{x\_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-35} \lor \neg \left(z \leq 8 \cdot 10^{+45}\right) \land z \leq 1.76 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ y (- t z)))) (t_2 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -0.32)
      t_2
      (if (<= z -2e-183)
        t_1
        (if (<= z 1.05e-273)
          (/ (* x_m y) t)
          (if (or (<= z 8.5e-35) (and (not (<= z 8e+45)) (<= z 1.76e+78)))
            t_1
            t_2)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y / (t - z));
	double t_2 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -0.32) {
		tmp = t_2;
	} else if (z <= -2e-183) {
		tmp = t_1;
	} else if (z <= 1.05e-273) {
		tmp = (x_m * y) / t;
	} else if ((z <= 8.5e-35) || (!(z <= 8e+45) && (z <= 1.76e+78))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m * (y / (t - z))
    t_2 = x_m * (1.0d0 - (y / z))
    if (z <= (-0.32d0)) then
        tmp = t_2
    else if (z <= (-2d-183)) then
        tmp = t_1
    else if (z <= 1.05d-273) then
        tmp = (x_m * y) / t
    else if ((z <= 8.5d-35) .or. (.not. (z <= 8d+45)) .and. (z <= 1.76d+78)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y / (t - z));
	double t_2 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -0.32) {
		tmp = t_2;
	} else if (z <= -2e-183) {
		tmp = t_1;
	} else if (z <= 1.05e-273) {
		tmp = (x_m * y) / t;
	} else if ((z <= 8.5e-35) || (!(z <= 8e+45) && (z <= 1.76e+78))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (y / (t - z))
	t_2 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -0.32:
		tmp = t_2
	elif z <= -2e-183:
		tmp = t_1
	elif z <= 1.05e-273:
		tmp = (x_m * y) / t
	elif (z <= 8.5e-35) or (not (z <= 8e+45) and (z <= 1.76e+78)):
		tmp = t_1
	else:
		tmp = t_2
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(y / Float64(t - z)))
	t_2 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -0.32)
		tmp = t_2;
	elseif (z <= -2e-183)
		tmp = t_1;
	elseif (z <= 1.05e-273)
		tmp = Float64(Float64(x_m * y) / t);
	elseif ((z <= 8.5e-35) || (!(z <= 8e+45) && (z <= 1.76e+78)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (y / (t - z));
	t_2 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -0.32)
		tmp = t_2;
	elseif (z <= -2e-183)
		tmp = t_1;
	elseif (z <= 1.05e-273)
		tmp = (x_m * y) / t;
	elseif ((z <= 8.5e-35) || (~((z <= 8e+45)) && (z <= 1.76e+78)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -0.32], t$95$2, If[LessEqual[z, -2e-183], t$95$1, If[LessEqual[z, 1.05e-273], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 8.5e-35], And[N[Not[LessEqual[z, 8e+45]], $MachinePrecision], LessEqual[z, 1.76e+78]]], t$95$1, t$95$2]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.320000000000000007 or 8.5000000000000001e-35 < z < 7.9999999999999994e45 or 1.76e78 < z

   1. Initial program 79.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 75.6%

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

      3. associate-*l* 75.6%

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

      4. associate-*l/ 75.6%

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

      5. *-commutative 75.6%

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

      6. neg-mul-1 75.6%

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

      7. neg-sub0 75.6%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      8. associate--r- 75.6%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      9. neg-sub0 75.6%

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

      10. +-commutative 75.6%

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

      11. sub-neg 75.6%

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

      12. div-sub 75.6%

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

      13. *-inverses 75.6%

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

   7. Simplified 75.6%

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

   if -0.320000000000000007 < z < -2.00000000000000001e-183 or 1.0500000000000001e-273 < z < 8.5000000000000001e-35 or 7.9999999999999994e45 < z < 1.76e78

   1. Initial program 88.4%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around inf 73.2%

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

      1. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

   if -2.00000000000000001e-183 < z < 1.0500000000000001e-273

   1. Initial program 94.9%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in z around 0 85.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.32:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-273}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-35} \lor \neg \left(z \leq 8 \cdot 10^{+45}\right) \land z \leq 1.76 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+21} \lor \neg \left(y \leq -0.0013\right) \land \left(y \leq -1.65 \cdot 10^{-24} \lor \neg \left(y \leq 7 \cdot 10^{+63}\right)\right):\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= y -2.6e+21)
          (and (not (<= y -0.0013)) (or (<= y -1.65e-24) (not (<= y 7e+63)))))
    (* x_m (/ y (- t z)))
    (* x_m (/ z (- z t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e+21) || (!(y <= -0.0013) && ((y <= -1.65e-24) || !(y <= 7e+63)))) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = x_m * (z / (z - t));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.6d+21)) .or. (.not. (y <= (-0.0013d0))) .and. (y <= (-1.65d-24)) .or. (.not. (y <= 7d+63))) then
        tmp = x_m * (y / (t - z))
    else
        tmp = x_m * (z / (z - t))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e+21) || (!(y <= -0.0013) && ((y <= -1.65e-24) || !(y <= 7e+63)))) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = x_m * (z / (z - t));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (y <= -2.6e+21) or (not (y <= -0.0013) and ((y <= -1.65e-24) or not (y <= 7e+63))):
		tmp = x_m * (y / (t - z))
	else:
		tmp = x_m * (z / (z - t))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e+21) || (!(y <= -0.0013) && ((y <= -1.65e-24) || !(y <= 7e+63))))
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x_m * Float64(z / Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((y <= -2.6e+21) || (~((y <= -0.0013)) && ((y <= -1.65e-24) || ~((y <= 7e+63)))))
		tmp = x_m * (y / (t - z));
	else
		tmp = x_m * (z / (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[y, -2.6e+21], And[N[Not[LessEqual[y, -0.0013]], $MachinePrecision], Or[LessEqual[y, -1.65e-24], N[Not[LessEqual[y, 7e+63]], $MachinePrecision]]]], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e21 or -0.0012999999999999999 < y < -1.64999999999999992e-24 or 7.00000000000000059e63 < y

   1. Initial program 82.9%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

   if -2.6e21 < y < -0.0012999999999999999 or -1.64999999999999992e-24 < y < 7.00000000000000059e63

   1. Initial program 86.1%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-neg-frac2 71.6%

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

      3. neg-sub0 71.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.6%

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

      6. mul-1-neg 71.6%

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

      7. +-commutative 71.6%

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

      8. mul-1-neg 71.6%

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

      9. sub-neg 71.6%

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

      10. associate-/l* 82.0%

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

   7. Simplified 82.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+21} \lor \neg \left(y \leq -0.0013\right) \land \left(y \leq -1.65 \cdot 10^{-24} \lor \neg \left(y \leq 7 \cdot 10^{+63}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0027:\\ \;\;\;\;\frac{x\_m}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-24} \lor \neg \left(y \leq 1.5 \cdot 10^{+63}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ y (- t z)))))
   (*
    x_s
    (if (<= y -4.7e+21)
      t_1
      (if (<= y -0.0027)
        (/ x_m (- 1.0 (/ t z)))
        (if (or (<= y -7e-24) (not (<= y 1.5e+63)))
          t_1
          (* x_m (/ z (- z t)))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y / (t - z));
	double tmp;
	if (y <= -4.7e+21) {
		tmp = t_1;
	} else if (y <= -0.0027) {
		tmp = x_m / (1.0 - (t / z));
	} else if ((y <= -7e-24) || !(y <= 1.5e+63)) {
		tmp = t_1;
	} else {
		tmp = x_m * (z / (z - t));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m * (y / (t - z))
    if (y <= (-4.7d+21)) then
        tmp = t_1
    else if (y <= (-0.0027d0)) then
        tmp = x_m / (1.0d0 - (t / z))
    else if ((y <= (-7d-24)) .or. (.not. (y <= 1.5d+63))) then
        tmp = t_1
    else
        tmp = x_m * (z / (z - t))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y / (t - z));
	double tmp;
	if (y <= -4.7e+21) {
		tmp = t_1;
	} else if (y <= -0.0027) {
		tmp = x_m / (1.0 - (t / z));
	} else if ((y <= -7e-24) || !(y <= 1.5e+63)) {
		tmp = t_1;
	} else {
		tmp = x_m * (z / (z - t));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (y / (t - z))
	tmp = 0
	if y <= -4.7e+21:
		tmp = t_1
	elif y <= -0.0027:
		tmp = x_m / (1.0 - (t / z))
	elif (y <= -7e-24) or not (y <= 1.5e+63):
		tmp = t_1
	else:
		tmp = x_m * (z / (z - t))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -4.7e+21)
		tmp = t_1;
	elseif (y <= -0.0027)
		tmp = Float64(x_m / Float64(1.0 - Float64(t / z)));
	elseif ((y <= -7e-24) || !(y <= 1.5e+63))
		tmp = t_1;
	else
		tmp = Float64(x_m * Float64(z / Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (y / (t - z));
	tmp = 0.0;
	if (y <= -4.7e+21)
		tmp = t_1;
	elseif (y <= -0.0027)
		tmp = x_m / (1.0 - (t / z));
	elseif ((y <= -7e-24) || ~((y <= 1.5e+63)))
		tmp = t_1;
	else
		tmp = x_m * (z / (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -4.7e+21], t$95$1, If[LessEqual[y, -0.0027], N[(x$95$m / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -7e-24], N[Not[LessEqual[y, 1.5e+63]], $MachinePrecision]], t$95$1, N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7e21 or -0.0027000000000000001 < y < -6.9999999999999993e-24 or 1.5e63 < y

   1. Initial program 82.9%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

   if -4.7e21 < y < -0.0027000000000000001

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. distribute-neg-frac2 87.5%

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

      3. neg-sub0 87.5%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 87.5%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 87.5%

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

      6. mul-1-neg 87.5%

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

      7. +-commutative 87.5%

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

      8. mul-1-neg 87.5%

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

      9. sub-neg 87.5%

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

      10. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0 87.5%

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

      1. associate-*l/ 75.6%

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

      2. associate-/r/ 87.8%

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

      3. div-sub 87.8%

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

      4. *-inverses 87.8%

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

   10. Simplified 87.8%

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

   if -6.9999999999999993e-24 < y < 1.5e63

   1. Initial program 85.3%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-neg-frac2 70.6%

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

      3. neg-sub0 70.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 70.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 70.6%

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

      6. mul-1-neg 70.6%

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

      7. +-commutative 70.6%

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

      8. mul-1-neg 70.6%

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

      9. sub-neg 70.6%

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

      10. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -0.0027:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-24} \lor \neg \left(y \leq 1.5 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0032:\\ \;\;\;\;\frac{x\_m}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\frac{t - z}{y}}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ y (- t z)))))
   (*
    x_s
    (if (<= y -4.1e+20)
      t_1
      (if (<= y -0.0032)
        (/ x_m (- 1.0 (/ t z)))
        (if (<= y -2.3e-24)
          t_1
          (if (<= y 5e+62) (* x_m (/ z (- z t))) (/ x_m (/ (- t z) y)))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y / (t - z));
	double tmp;
	if (y <= -4.1e+20) {
		tmp = t_1;
	} else if (y <= -0.0032) {
		tmp = x_m / (1.0 - (t / z));
	} else if (y <= -2.3e-24) {
		tmp = t_1;
	} else if (y <= 5e+62) {
		tmp = x_m * (z / (z - t));
	} else {
		tmp = x_m / ((t - z) / y);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    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_m * (y / (t - z))
    if (y <= (-4.1d+20)) then
        tmp = t_1
    else if (y <= (-0.0032d0)) then
        tmp = x_m / (1.0d0 - (t / z))
    else if (y <= (-2.3d-24)) then
        tmp = t_1
    else if (y <= 5d+62) then
        tmp = x_m * (z / (z - t))
    else
        tmp = x_m / ((t - z) / y)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (y / (t - z));
	double tmp;
	if (y <= -4.1e+20) {
		tmp = t_1;
	} else if (y <= -0.0032) {
		tmp = x_m / (1.0 - (t / z));
	} else if (y <= -2.3e-24) {
		tmp = t_1;
	} else if (y <= 5e+62) {
		tmp = x_m * (z / (z - t));
	} else {
		tmp = x_m / ((t - z) / y);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (y / (t - z))
	tmp = 0
	if y <= -4.1e+20:
		tmp = t_1
	elif y <= -0.0032:
		tmp = x_m / (1.0 - (t / z))
	elif y <= -2.3e-24:
		tmp = t_1
	elif y <= 5e+62:
		tmp = x_m * (z / (z - t))
	else:
		tmp = x_m / ((t - z) / y)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -4.1e+20)
		tmp = t_1;
	elseif (y <= -0.0032)
		tmp = Float64(x_m / Float64(1.0 - Float64(t / z)));
	elseif (y <= -2.3e-24)
		tmp = t_1;
	elseif (y <= 5e+62)
		tmp = Float64(x_m * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x_m / Float64(Float64(t - z) / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (y / (t - z));
	tmp = 0.0;
	if (y <= -4.1e+20)
		tmp = t_1;
	elseif (y <= -0.0032)
		tmp = x_m / (1.0 - (t / z));
	elseif (y <= -2.3e-24)
		tmp = t_1;
	elseif (y <= 5e+62)
		tmp = x_m * (z / (z - t));
	else
		tmp = x_m / ((t - z) / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -4.1e+20], t$95$1, If[LessEqual[y, -0.0032], N[(x$95$m / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-24], t$95$1, If[LessEqual[y, 5e+62], N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -4.1e20 or -0.00320000000000000015 < y < -2.3000000000000001e-24

   1. Initial program 83.7%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around inf 71.1%

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

      1. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   if -4.1e20 < y < -0.00320000000000000015

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. distribute-neg-frac2 87.5%

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

      3. neg-sub0 87.5%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 87.5%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 87.5%

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

      6. mul-1-neg 87.5%

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

      7. +-commutative 87.5%

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

      8. mul-1-neg 87.5%

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

      9. sub-neg 87.5%

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

      10. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0 87.5%

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

      1. associate-*l/ 75.6%

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

      2. associate-/r/ 87.8%

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

      3. div-sub 87.8%

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

      4. *-inverses 87.8%

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

   10. Simplified 87.8%

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

   if -2.3000000000000001e-24 < y < 5.00000000000000029e62

   1. Initial program 85.3%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-neg-frac2 70.6%

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

      3. neg-sub0 70.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 70.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 70.6%

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

      6. mul-1-neg 70.6%

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

      7. +-commutative 70.6%

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

      8. mul-1-neg 70.6%

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

      9. sub-neg 70.6%

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

      10. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

   if 5.00000000000000029e62 < y

   1. Initial program 81.7%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

      1. clear-num 93.4%

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

      2. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in y around inf 87.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -0.0032:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+20}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -0.00172:\\ \;\;\;\;\frac{x\_m}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{x\_m \cdot y}{t - z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+63}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -4.3e+20)
    (* x_m (/ y (- t z)))
    (if (<= y -0.00172)
      (/ x_m (- 1.0 (/ t z)))
      (if (<= y -8.5e-25)
        (/ (* x_m y) (- t z))
        (if (<= y 5e+63) (* x_m (/ z (- z t))) (/ x_m (/ (- t z) y))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.3e+20) {
		tmp = x_m * (y / (t - z));
	} else if (y <= -0.00172) {
		tmp = x_m / (1.0 - (t / z));
	} else if (y <= -8.5e-25) {
		tmp = (x_m * y) / (t - z);
	} else if (y <= 5e+63) {
		tmp = x_m * (z / (z - t));
	} else {
		tmp = x_m / ((t - z) / y);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.3d+20)) then
        tmp = x_m * (y / (t - z))
    else if (y <= (-0.00172d0)) then
        tmp = x_m / (1.0d0 - (t / z))
    else if (y <= (-8.5d-25)) then
        tmp = (x_m * y) / (t - z)
    else if (y <= 5d+63) then
        tmp = x_m * (z / (z - t))
    else
        tmp = x_m / ((t - z) / y)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.3e+20) {
		tmp = x_m * (y / (t - z));
	} else if (y <= -0.00172) {
		tmp = x_m / (1.0 - (t / z));
	} else if (y <= -8.5e-25) {
		tmp = (x_m * y) / (t - z);
	} else if (y <= 5e+63) {
		tmp = x_m * (z / (z - t));
	} else {
		tmp = x_m / ((t - z) / y);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -4.3e+20:
		tmp = x_m * (y / (t - z))
	elif y <= -0.00172:
		tmp = x_m / (1.0 - (t / z))
	elif y <= -8.5e-25:
		tmp = (x_m * y) / (t - z)
	elif y <= 5e+63:
		tmp = x_m * (z / (z - t))
	else:
		tmp = x_m / ((t - z) / y)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -4.3e+20)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	elseif (y <= -0.00172)
		tmp = Float64(x_m / Float64(1.0 - Float64(t / z)));
	elseif (y <= -8.5e-25)
		tmp = Float64(Float64(x_m * y) / Float64(t - z));
	elseif (y <= 5e+63)
		tmp = Float64(x_m * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x_m / Float64(Float64(t - z) / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -4.3e+20)
		tmp = x_m * (y / (t - z));
	elseif (y <= -0.00172)
		tmp = x_m / (1.0 - (t / z));
	elseif (y <= -8.5e-25)
		tmp = (x_m * y) / (t - z);
	elseif (y <= 5e+63)
		tmp = x_m * (z / (z - t));
	else
		tmp = x_m / ((t - z) / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -4.3e+20], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00172], N[(x$95$m / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-25], N[(N[(x$95$m * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+63], N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -4.3e20

   1. Initial program 81.4%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around inf 68.7%

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

      1. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

   if -4.3e20 < y < -0.00171999999999999996

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. distribute-neg-frac2 87.5%

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

      3. neg-sub0 87.5%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 87.5%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 87.5%

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

      6. mul-1-neg 87.5%

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

      7. +-commutative 87.5%

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

      8. mul-1-neg 87.5%

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

      9. sub-neg 87.5%

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

      10. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0 87.5%

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

      1. associate-*l/ 75.6%

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

      2. associate-/r/ 87.8%

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

      3. div-sub 87.8%

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

      4. *-inverses 87.8%

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

   10. Simplified 87.8%

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

   if -0.00171999999999999996 < y < -8.49999999999999981e-25

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 88.3%

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

   if -8.49999999999999981e-25 < y < 5.00000000000000011e63

   1. Initial program 85.3%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-neg-frac2 70.6%

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

      3. neg-sub0 70.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 70.6%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 70.6%

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

      6. mul-1-neg 70.6%

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

      7. +-commutative 70.6%

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

      8. mul-1-neg 70.6%

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

      9. sub-neg 70.6%

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

      10. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

   if 5.00000000000000011e63 < y

   1. Initial program 81.7%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

      1. clear-num 93.4%

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

      2. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in y around inf 87.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -0.00172:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-13} \lor \neg \left(z \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -8e-13) (not (<= z 2e-32)))
    (* x_m (- 1.0 (/ y z)))
    (/ x_m (/ t y)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-13) || !(z <= 2e-32)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = x_m / (t / y);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d-13)) .or. (.not. (z <= 2d-32))) then
        tmp = x_m * (1.0d0 - (y / z))
    else
        tmp = x_m / (t / y)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-13) || !(z <= 2e-32)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = x_m / (t / y);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -8e-13) or not (z <= 2e-32):
		tmp = x_m * (1.0 - (y / z))
	else:
		tmp = x_m / (t / y)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -8e-13) || !(z <= 2e-32))
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x_m / Float64(t / y));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -8e-13) || ~((z <= 2e-32)))
		tmp = x_m * (1.0 - (y / z));
	else
		tmp = x_m / (t / y);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -8e-13], N[Not[LessEqual[z, 2e-32]], $MachinePrecision]], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(t / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000002e-13 or 2.00000000000000011e-32 < z

   1. Initial program 78.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 58.9%

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

      1. *-commutative 58.9%

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

      2. associate-/l* 72.3%

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

      3. associate-*l* 72.3%

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

      4. associate-*l/ 72.3%

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

      5. *-commutative 72.3%

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

      6. neg-mul-1 72.3%

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

      7. neg-sub0 72.3%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      8. associate--r- 72.3%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      9. neg-sub0 72.3%

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

      10. +-commutative 72.3%

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

      11. sub-neg 72.3%

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

      12. div-sub 72.3%

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

      13. *-inverses 72.3%

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

   7. Simplified 72.3%

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

   if -8.0000000000000002e-13 < z < 2.00000000000000011e-32

   1. Initial program 92.1%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

      1. clear-num 89.5%

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

      2. un-div-inv 90.3%

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

   6. Applied egg-rr 90.3%

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

   7. Taylor expanded in z around 0 69.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-13} \lor \neg \left(z \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+24}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+77}:\\ \;\;\;\;x\_m \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -8.8e+24) x_m (if (<= z 8.5e+77) (* x_m (/ y t)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -8.8e+24) {
		tmp = x_m;
	} else if (z <= 8.5e+77) {
		tmp = x_m * (y / t);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8.8d+24)) then
        tmp = x_m
    else if (z <= 8.5d+77) then
        tmp = x_m * (y / t)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -8.8e+24) {
		tmp = x_m;
	} else if (z <= 8.5e+77) {
		tmp = x_m * (y / t);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -8.8e+24:
		tmp = x_m
	elif z <= 8.5e+77:
		tmp = x_m * (y / t)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -8.8e+24)
		tmp = x_m;
	elseif (z <= 8.5e+77)
		tmp = Float64(x_m * Float64(y / t));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -8.8e+24)
		tmp = x_m;
	elseif (z <= 8.5e+77)
		tmp = x_m * (y / t);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -8.8e+24], x$95$m, If[LessEqual[z, 8.5e+77], N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000007e24 or 8.50000000000000018e77 < z

   1. Initial program 76.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.2%

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

   if -8.80000000000000007e24 < z < 8.50000000000000018e77

   1. Initial program 91.7%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in z around 0 61.5%

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

      1. associate-/l* 63.3%

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

   7. Simplified 63.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+23}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{x\_m}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -4e+23) x_m (if (<= z 6.2e+77) (/ x_m (/ t y)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -4e+23) {
		tmp = x_m;
	} else if (z <= 6.2e+77) {
		tmp = x_m / (t / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4d+23)) then
        tmp = x_m
    else if (z <= 6.2d+77) then
        tmp = x_m / (t / y)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -4e+23) {
		tmp = x_m;
	} else if (z <= 6.2e+77) {
		tmp = x_m / (t / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -4e+23:
		tmp = x_m
	elif z <= 6.2e+77:
		tmp = x_m / (t / y)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -4e+23)
		tmp = x_m;
	elseif (z <= 6.2e+77)
		tmp = Float64(x_m / Float64(t / y));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -4e+23)
		tmp = x_m;
	elseif (z <= 6.2e+77)
		tmp = x_m / (t / y);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -4e+23], x$95$m, If[LessEqual[z, 6.2e+77], N[(x$95$m / N[(t / y), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999997e23 or 6.19999999999999997e77 < z

   1. Initial program 76.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.2%

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

   if -3.9999999999999997e23 < z < 6.19999999999999997e77

   1. Initial program 91.7%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

      1. clear-num 91.6%

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

      2. un-div-inv 92.3%

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

   6. Applied egg-rr 92.3%

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

   7. Taylor expanded in z around 0 63.4%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x\_m \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x\_m}{z - t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.05e+20)
    (* x_m (/ (- y z) (- t z)))
    (* (- z y) (/ x_m (- z t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.05e+20) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (z - y) * (x_m / (z - t));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 1.05d+20) then
        tmp = x_m * ((y - z) / (t - z))
    else
        tmp = (z - y) * (x_m / (z - t))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.05e+20) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (z - y) * (x_m / (z - t));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 1.05e+20:
		tmp = x_m * ((y - z) / (t - z))
	else:
		tmp = (z - y) * (x_m / (z - t))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1.05e+20)
		tmp = Float64(x_m * Float64(Float64(y - z) / Float64(t - z)));
	else
		tmp = Float64(Float64(z - y) * Float64(x_m / Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 1.05e+20)
		tmp = x_m * ((y - z) / (t - z));
	else
		tmp = (z - y) * (x_m / (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1.05e+20], N[(x$95$m * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(x$95$m / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.05e20

   1. Initial program 89.7%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   if 1.05e20 < x

   1. Initial program 68.7%

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

      1. remove-double-neg 68.7%

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

      2. distribute-lft-neg-out 68.7%

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

      3. distribute-neg-frac 68.7%

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

      4. distribute-neg-frac2 68.7%

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

      5. distribute-lft-neg-out 68.7%

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

      6. distribute-rgt-neg-in 68.7%

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

      7. sub-neg 68.7%

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

      8. distribute-neg-in 68.7%

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

      9. remove-double-neg 68.7%

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

      10. +-commutative 68.7%

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

      11. sub-neg 68.7%

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

      12. sub-neg 68.7%

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

      13. distribute-neg-in 68.7%

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

      14. remove-double-neg 68.7%

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

      15. +-commutative 68.7%

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

      16. sub-neg 68.7%

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

   3. Simplified 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 96.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{+19}:\\ \;\;\;\;\frac{x\_m}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x\_m}{z - t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1e+19) (/ x_m (/ (- t z) (- y z))) (* (- z y) (/ x_m (- z t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1e+19) {
		tmp = x_m / ((t - z) / (y - z));
	} else {
		tmp = (z - y) * (x_m / (z - t));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 1d+19) then
        tmp = x_m / ((t - z) / (y - z))
    else
        tmp = (z - y) * (x_m / (z - t))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1e+19) {
		tmp = x_m / ((t - z) / (y - z));
	} else {
		tmp = (z - y) * (x_m / (z - t));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 1e+19:
		tmp = x_m / ((t - z) / (y - z))
	else:
		tmp = (z - y) * (x_m / (z - t))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1e+19)
		tmp = Float64(x_m / Float64(Float64(t - z) / Float64(y - z)));
	else
		tmp = Float64(Float64(z - y) * Float64(x_m / Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 1e+19)
		tmp = x_m / ((t - z) / (y - z));
	else
		tmp = (z - y) * (x_m / (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1e+19], N[(x$95$m / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(x$95$m / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1e19

   1. Initial program 89.7%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.3%

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

   6. Applied egg-rr 96.3%

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

   if 1e19 < x

   1. Initial program 68.7%

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

      1. remove-double-neg 68.7%

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

      2. distribute-lft-neg-out 68.7%

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

      3. distribute-neg-frac 68.7%

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

      4. distribute-neg-frac2 68.7%

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

      5. distribute-lft-neg-out 68.7%

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

      6. distribute-rgt-neg-in 68.7%

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

      7. sub-neg 68.7%

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

      8. distribute-neg-in 68.7%

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

      9. remove-double-neg 68.7%

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

      10. +-commutative 68.7%

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

      11. sub-neg 68.7%

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

      12. sub-neg 68.7%

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

      13. distribute-neg-in 68.7%

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

      14. remove-double-neg 68.7%

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

      15. +-commutative 68.7%

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

      16. sub-neg 68.7%

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

   3. Simplified 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+19}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x\_m}{z - t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.4e-11)
    (/ (* x_m (- y z)) (- t z))
    (* (- z y) (/ x_m (- z t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.4e-11) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (z - y) * (x_m / (z - t));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 1.4d-11) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (z - y) * (x_m / (z - t))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.4e-11) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (z - y) * (x_m / (z - t));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 1.4e-11:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (z - y) * (x_m / (z - t))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1.4e-11)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(z - y) * Float64(x_m / Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 1.4e-11)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (z - y) * (x_m / (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1.4e-11], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(x$95$m / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.4e-11

   1. Initial program 89.2%

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

   if 1.4e-11 < x

   1. Initial program 72.7%

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

      1. remove-double-neg 72.7%

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

      2. distribute-lft-neg-out 72.7%

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

      3. distribute-neg-frac 72.7%

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

      4. distribute-neg-frac2 72.7%

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

      5. distribute-lft-neg-out 72.7%

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

      6. distribute-rgt-neg-in 72.7%

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

      7. sub-neg 72.7%

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

      8. distribute-neg-in 72.7%

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

      9. remove-double-neg 72.7%

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

      10. +-commutative 72.7%

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

      11. sub-neg 72.7%

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

      12. sub-neg 72.7%

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

      13. distribute-neg-in 72.7%

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

      14. remove-double-neg 72.7%

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

      15. +-commutative 72.7%

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

      16. sub-neg 72.7%

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

   3. Simplified 72.7%

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

      1. *-commutative 72.7%

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

      2. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(x\_m \cdot \frac{y - z}{t - z}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (* x_m (/ (- y z) (- t z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m * ((y - z) / (t - z)));
}

Fortran

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

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m * ((y - z) / (t - z)));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * (x_m * ((y - z) / (t - z)))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(x_m * Float64(Float64(y - z) / Float64(t - z))))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (x_m * ((y - z) / (t - z)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(x$95$m * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.7%

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

   1. associate-/l* 95.9%

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

3. Simplified 95.9%

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

5. Final simplification 95.9%

   \[\leadsto x \cdot \frac{y - z}{t - z} \]
6. Add Preprocessing

Alternative 14: 35.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s x_m))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * x_m;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * x_m
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * x_m;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * x_m

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * x_m)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * x_m;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 84.7%

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

   1. associate-/l* 95.9%

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

3. Simplified 95.9%

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

5. Taylor expanded in z around inf 33.2%

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

6. Final simplification 33.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.0% accurate, 1.0× 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 2024052 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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