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

Percentage Accurate: 84.8% → 96.7%

Time: 8.0s

Alternatives: 15

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: 84.8% 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: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2e-26) (/ (* x_m (- y z)) (- t z)) (* (- y z) (/ x_m (- 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) {
	double tmp;
	if (x_m <= 2e-26) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (y - z) * (x_m / (t - z));
	}
	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 <= 2d-26) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (y - z) * (x_m / (t - z))
    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 <= 2e-26) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (y - z) * (x_m / (t - z));
	}
	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 <= 2e-26:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (y - z) * (x_m / (t - z))
	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 <= 2e-26)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(y - z) * Float64(x_m / Float64(t - z)));
	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 <= 2e-26)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (y - z) * (x_m / (t - z));
	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, 2e-26], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.0000000000000001e-26

   1. Initial program 88.1%

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

   if 2.0000000000000001e-26 < x

   1. Initial program 65.4%

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

      1. associate-*r/ 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-/l* 98.2%

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

   6. Applied egg-rr 98.2%

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

Alternative 2: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{x\_m}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-201}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x\_m}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-209}:\\ \;\;\;\;\frac{x\_m \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{x\_m}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -2.9e+16)
    (/ x_m (/ z (- z y)))
    (if (<= z -2.75e-201)
      (/ (- y z) (/ t x_m))
      (if (<= z 2.15e-209)
        (/ (* x_m y) (- t z))
        (if (<= z 7.6e-60) (/ x_m (/ t (- y z))) (* x_m (- 1.0 (/ y 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) {
	double tmp;
	if (z <= -2.9e+16) {
		tmp = x_m / (z / (z - y));
	} else if (z <= -2.75e-201) {
		tmp = (y - z) / (t / x_m);
	} else if (z <= 2.15e-209) {
		tmp = (x_m * y) / (t - z);
	} else if (z <= 7.6e-60) {
		tmp = x_m / (t / (y - z));
	} else {
		tmp = x_m * (1.0 - (y / z));
	}
	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 <= (-2.9d+16)) then
        tmp = x_m / (z / (z - y))
    else if (z <= (-2.75d-201)) then
        tmp = (y - z) / (t / x_m)
    else if (z <= 2.15d-209) then
        tmp = (x_m * y) / (t - z)
    else if (z <= 7.6d-60) then
        tmp = x_m / (t / (y - z))
    else
        tmp = x_m * (1.0d0 - (y / z))
    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 <= -2.9e+16) {
		tmp = x_m / (z / (z - y));
	} else if (z <= -2.75e-201) {
		tmp = (y - z) / (t / x_m);
	} else if (z <= 2.15e-209) {
		tmp = (x_m * y) / (t - z);
	} else if (z <= 7.6e-60) {
		tmp = x_m / (t / (y - z));
	} else {
		tmp = x_m * (1.0 - (y / z));
	}
	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 <= -2.9e+16:
		tmp = x_m / (z / (z - y))
	elif z <= -2.75e-201:
		tmp = (y - z) / (t / x_m)
	elif z <= 2.15e-209:
		tmp = (x_m * y) / (t - z)
	elif z <= 7.6e-60:
		tmp = x_m / (t / (y - z))
	else:
		tmp = x_m * (1.0 - (y / z))
	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 <= -2.9e+16)
		tmp = Float64(x_m / Float64(z / Float64(z - y)));
	elseif (z <= -2.75e-201)
		tmp = Float64(Float64(y - z) / Float64(t / x_m));
	elseif (z <= 2.15e-209)
		tmp = Float64(Float64(x_m * y) / Float64(t - z));
	elseif (z <= 7.6e-60)
		tmp = Float64(x_m / Float64(t / Float64(y - z)));
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	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 <= -2.9e+16)
		tmp = x_m / (z / (z - y));
	elseif (z <= -2.75e-201)
		tmp = (y - z) / (t / x_m);
	elseif (z <= 2.15e-209)
		tmp = (x_m * y) / (t - z);
	elseif (z <= 7.6e-60)
		tmp = x_m / (t / (y - z));
	else
		tmp = x_m * (1.0 - (y / z));
	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, -2.9e+16], N[(x$95$m / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.75e-201], N[(N[(y - z), $MachinePrecision] / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-209], N[(N[(x$95$m * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-60], N[(x$95$m / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if z < -2.9e16

   1. Initial program 71.2%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-neg-frac2 80.1%

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

   9. Simplified 80.1%

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

   if -2.9e16 < z < -2.75000000000000017e-201

   1. Initial program 88.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 91.1%

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

      2. associate-/r/ 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in t around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*r/ 79.5%

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

   9. Simplified 79.5%

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

       1. clear-num 79.5%

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

       2. un-div-inv 79.6%

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

   11. Applied egg-rr 79.6%

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

   if -2.75000000000000017e-201 < z < 2.15000000000000003e-209

   1. Initial program 97.9%

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

      1. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in y around inf 94.4%

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

   if 2.15000000000000003e-209 < z < 7.59999999999999989e-60

   1. Initial program 84.3%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 94.4%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in t around inf 83.5%

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

   if 7.59999999999999989e-60 < z

   1. Initial program 76.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.3%

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

      1. mul-1-neg 66.3%

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

      2. associate-/l* 83.7%

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

      3. distribute-rgt-neg-in 83.7%

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

      4. div-sub 83.7%

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

      5. sub-neg 83.7%

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

      6. *-inverses 83.7%

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

      7. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in x around 0 83.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-201}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-209}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-201}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x\_m}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-209}:\\ \;\;\;\;\frac{x\_m \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x\_m}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -3.6e+15)
      t_1
      (if (<= z -1.32e-201)
        (/ (- y z) (/ t x_m))
        (if (<= z 1.95e-209)
          (/ (* x_m y) (- t z))
          (if (<= z 9.2e-61) (/ x_m (/ t (- y z))) t_1)))))))

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 * (1.0 - (y / z));
	double tmp;
	if (z <= -3.6e+15) {
		tmp = t_1;
	} else if (z <= -1.32e-201) {
		tmp = (y - z) / (t / x_m);
	} else if (z <= 1.95e-209) {
		tmp = (x_m * y) / (t - z);
	} else if (z <= 9.2e-61) {
		tmp = x_m / (t / (y - z));
	} else {
		tmp = t_1;
	}
	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 * (1.0d0 - (y / z))
    if (z <= (-3.6d+15)) then
        tmp = t_1
    else if (z <= (-1.32d-201)) then
        tmp = (y - z) / (t / x_m)
    else if (z <= 1.95d-209) then
        tmp = (x_m * y) / (t - z)
    else if (z <= 9.2d-61) then
        tmp = x_m / (t / (y - z))
    else
        tmp = t_1
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -3.6e+15) {
		tmp = t_1;
	} else if (z <= -1.32e-201) {
		tmp = (y - z) / (t / x_m);
	} else if (z <= 1.95e-209) {
		tmp = (x_m * y) / (t - z);
	} else if (z <= 9.2e-61) {
		tmp = x_m / (t / (y - z));
	} else {
		tmp = t_1;
	}
	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 * (1.0 - (y / z))
	tmp = 0
	if z <= -3.6e+15:
		tmp = t_1
	elif z <= -1.32e-201:
		tmp = (y - z) / (t / x_m)
	elif z <= 1.95e-209:
		tmp = (x_m * y) / (t - z)
	elif z <= 9.2e-61:
		tmp = x_m / (t / (y - z))
	else:
		tmp = t_1
	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(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.6e+15)
		tmp = t_1;
	elseif (z <= -1.32e-201)
		tmp = Float64(Float64(y - z) / Float64(t / x_m));
	elseif (z <= 1.95e-209)
		tmp = Float64(Float64(x_m * y) / Float64(t - z));
	elseif (z <= 9.2e-61)
		tmp = Float64(x_m / Float64(t / Float64(y - z)));
	else
		tmp = t_1;
	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 * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.6e+15)
		tmp = t_1;
	elseif (z <= -1.32e-201)
		tmp = (y - z) / (t / x_m);
	elseif (z <= 1.95e-209)
		tmp = (x_m * y) / (t - z);
	elseif (z <= 9.2e-61)
		tmp = x_m / (t / (y - z));
	else
		tmp = t_1;
	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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -3.6e+15], t$95$1, If[LessEqual[z, -1.32e-201], N[(N[(y - z), $MachinePrecision] / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-209], N[(N[(x$95$m * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-61], N[(x$95$m / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e15 or 9.19999999999999967e-61 < z

   1. Initial program 74.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-/l* 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

      4. div-sub 82.3%

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

      5. sub-neg 82.3%

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

      6. *-inverses 82.3%

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

      7. metadata-eval 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in x around 0 82.3%

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

   if -3.6e15 < z < -1.31999999999999996e-201

   1. Initial program 88.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 91.1%

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

      2. associate-/r/ 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in t around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*r/ 79.5%

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

   9. Simplified 79.5%

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

       1. clear-num 79.5%

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

       2. un-div-inv 79.6%

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

   11. Applied egg-rr 79.6%

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

   if -1.31999999999999996e-201 < z < 1.95e-209

   1. Initial program 97.9%

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

      1. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in y around inf 94.4%

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

   if 1.95e-209 < z < 9.19999999999999967e-61

   1. Initial program 84.3%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 94.4%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in t around inf 83.5%

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

Alternative 4: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-204}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-209}:\\ \;\;\;\;\frac{x\_m \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-60}:\\ \;\;\;\;\frac{x\_m}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -1.05e+20)
      t_1
      (if (<= z -1.55e-204)
        (* (- y z) (/ x_m t))
        (if (<= z 2.1e-209)
          (/ (* x_m y) (- t z))
          (if (<= z 8e-60) (/ x_m (/ t (- y z))) t_1)))))))

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 * (1.0 - (y / z));
	double tmp;
	if (z <= -1.05e+20) {
		tmp = t_1;
	} else if (z <= -1.55e-204) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 2.1e-209) {
		tmp = (x_m * y) / (t - z);
	} else if (z <= 8e-60) {
		tmp = x_m / (t / (y - z));
	} else {
		tmp = t_1;
	}
	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 * (1.0d0 - (y / z))
    if (z <= (-1.05d+20)) then
        tmp = t_1
    else if (z <= (-1.55d-204)) then
        tmp = (y - z) * (x_m / t)
    else if (z <= 2.1d-209) then
        tmp = (x_m * y) / (t - z)
    else if (z <= 8d-60) then
        tmp = x_m / (t / (y - z))
    else
        tmp = t_1
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -1.05e+20) {
		tmp = t_1;
	} else if (z <= -1.55e-204) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 2.1e-209) {
		tmp = (x_m * y) / (t - z);
	} else if (z <= 8e-60) {
		tmp = x_m / (t / (y - z));
	} else {
		tmp = t_1;
	}
	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 * (1.0 - (y / z))
	tmp = 0
	if z <= -1.05e+20:
		tmp = t_1
	elif z <= -1.55e-204:
		tmp = (y - z) * (x_m / t)
	elif z <= 2.1e-209:
		tmp = (x_m * y) / (t - z)
	elif z <= 8e-60:
		tmp = x_m / (t / (y - z))
	else:
		tmp = t_1
	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(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.05e+20)
		tmp = t_1;
	elseif (z <= -1.55e-204)
		tmp = Float64(Float64(y - z) * Float64(x_m / t));
	elseif (z <= 2.1e-209)
		tmp = Float64(Float64(x_m * y) / Float64(t - z));
	elseif (z <= 8e-60)
		tmp = Float64(x_m / Float64(t / Float64(y - z)));
	else
		tmp = t_1;
	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 * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.05e+20)
		tmp = t_1;
	elseif (z <= -1.55e-204)
		tmp = (y - z) * (x_m / t);
	elseif (z <= 2.1e-209)
		tmp = (x_m * y) / (t - z);
	elseif (z <= 8e-60)
		tmp = x_m / (t / (y - z));
	else
		tmp = t_1;
	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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.05e+20], t$95$1, If[LessEqual[z, -1.55e-204], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-209], N[(N[(x$95$m * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-60], N[(x$95$m / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e20 or 7.9999999999999998e-60 < z

   1. Initial program 74.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-/l* 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

      4. div-sub 82.3%

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

      5. sub-neg 82.3%

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

      6. *-inverses 82.3%

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

      7. metadata-eval 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in x around 0 82.3%

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

   if -1.05e20 < z < -1.55e-204

   1. Initial program 88.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 91.1%

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

      2. associate-/r/ 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in t around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*r/ 79.5%

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

   9. Simplified 79.5%

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

   if -1.55e-204 < z < 2.09999999999999996e-209

   1. Initial program 97.9%

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

      1. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in y around inf 94.4%

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

   if 2.09999999999999996e-209 < z < 7.9999999999999998e-60

   1. Initial program 84.3%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 94.4%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in t around inf 83.5%

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

Alternative 5: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-242}:\\ \;\;\;\;x\_m \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{x\_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-29}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -2.9e+18)
      t_1
      (if (<= z -2.9e-242)
        (* x_m (/ (- y z) t))
        (if (<= z 7.4e-234)
          (/ (* x_m y) t)
          (if (<= z 4.6e-29) (* x_m (/ y (- t z))) t_1)))))))

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 * (1.0 - (y / z));
	double tmp;
	if (z <= -2.9e+18) {
		tmp = t_1;
	} else if (z <= -2.9e-242) {
		tmp = x_m * ((y - z) / t);
	} else if (z <= 7.4e-234) {
		tmp = (x_m * y) / t;
	} else if (z <= 4.6e-29) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	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 * (1.0d0 - (y / z))
    if (z <= (-2.9d+18)) then
        tmp = t_1
    else if (z <= (-2.9d-242)) then
        tmp = x_m * ((y - z) / t)
    else if (z <= 7.4d-234) then
        tmp = (x_m * y) / t
    else if (z <= 4.6d-29) then
        tmp = x_m * (y / (t - z))
    else
        tmp = t_1
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -2.9e+18) {
		tmp = t_1;
	} else if (z <= -2.9e-242) {
		tmp = x_m * ((y - z) / t);
	} else if (z <= 7.4e-234) {
		tmp = (x_m * y) / t;
	} else if (z <= 4.6e-29) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	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 * (1.0 - (y / z))
	tmp = 0
	if z <= -2.9e+18:
		tmp = t_1
	elif z <= -2.9e-242:
		tmp = x_m * ((y - z) / t)
	elif z <= 7.4e-234:
		tmp = (x_m * y) / t
	elif z <= 4.6e-29:
		tmp = x_m * (y / (t - z))
	else:
		tmp = t_1
	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(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.9e+18)
		tmp = t_1;
	elseif (z <= -2.9e-242)
		tmp = Float64(x_m * Float64(Float64(y - z) / t));
	elseif (z <= 7.4e-234)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 4.6e-29)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	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 * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.9e+18)
		tmp = t_1;
	elseif (z <= -2.9e-242)
		tmp = x_m * ((y - z) / t);
	elseif (z <= 7.4e-234)
		tmp = (x_m * y) / t;
	elseif (z <= 4.6e-29)
		tmp = x_m * (y / (t - z));
	else
		tmp = t_1;
	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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -2.9e+18], t$95$1, If[LessEqual[z, -2.9e-242], N[(x$95$m * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-234], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.6e-29], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e18 or 4.59999999999999982e-29 < z

   1. Initial program 74.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 63.9%

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

      1. mul-1-neg 63.9%

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

      2. associate-/l* 82.6%

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

      3. distribute-rgt-neg-in 82.6%

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

      4. div-sub 82.6%

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

      5. sub-neg 82.6%

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

      6. *-inverses 82.6%

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

      7. metadata-eval 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in x around 0 82.6%

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

   if -2.9e18 < z < -2.9000000000000001e-242

   1. Initial program 91.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around inf 80.4%

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

      1. associate-/l* 82.1%

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

   7. Simplified 82.1%

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

   if -2.9000000000000001e-242 < z < 7.40000000000000025e-234

   1. Initial program 97.1%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around 0 83.6%

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

   if 7.40000000000000025e-234 < z < 4.59999999999999982e-29

   1. Initial program 87.5%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in y around inf 75.6%

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

      1. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

Alternative 6: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+15} \lor \neg \left(z \leq 4.6 \cdot 10^{-60}\right):\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -3.9e+15) (not (<= z 4.6e-60)))
    (* x_m (- 1.0 (/ y z)))
    (* (- y z) (/ x_m 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 ((z <= -3.9e+15) || !(z <= 4.6e-60)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = (y - z) * (x_m / 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 ((z <= (-3.9d+15)) .or. (.not. (z <= 4.6d-60))) then
        tmp = x_m * (1.0d0 - (y / z))
    else
        tmp = (y - z) * (x_m / 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 ((z <= -3.9e+15) || !(z <= 4.6e-60)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = (y - z) * (x_m / 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 (z <= -3.9e+15) or not (z <= 4.6e-60):
		tmp = x_m * (1.0 - (y / z))
	else:
		tmp = (y - z) * (x_m / 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 ((z <= -3.9e+15) || !(z <= 4.6e-60))
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x_m / 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 ((z <= -3.9e+15) || ~((z <= 4.6e-60)))
		tmp = x_m * (1.0 - (y / z));
	else
		tmp = (y - z) * (x_m / 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[z, -3.9e+15], N[Not[LessEqual[z, 4.6e-60]], $MachinePrecision]], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e15 or 4.6000000000000003e-60 < z

   1. Initial program 74.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-/l* 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

      4. div-sub 82.3%

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

      5. sub-neg 82.3%

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

      6. *-inverses 82.3%

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

      7. metadata-eval 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in x around 0 82.3%

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

   if -3.9e15 < z < 4.6000000000000003e-60

   1. Initial program 91.3%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 88.2%

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

      2. associate-/r/ 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in t around inf 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-*r/ 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+15} \lor \neg \left(z \leq 4.6 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+19} \lor \neg \left(z \leq 2.7 \cdot 10^{-29}\right):\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x\_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -8.5e+19) (not (<= z 2.7e-29)))
    (* x_m (- 1.0 (/ y z)))
    (* y (/ x_m (- 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) {
	double tmp;
	if ((z <= -8.5e+19) || !(z <= 2.7e-29)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = y * (x_m / (t - z));
	}
	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 <= (-8.5d+19)) .or. (.not. (z <= 2.7d-29))) then
        tmp = x_m * (1.0d0 - (y / z))
    else
        tmp = y * (x_m / (t - z))
    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 <= -8.5e+19) || !(z <= 2.7e-29)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = y * (x_m / (t - z));
	}
	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 <= -8.5e+19) or not (z <= 2.7e-29):
		tmp = x_m * (1.0 - (y / z))
	else:
		tmp = y * (x_m / (t - z))
	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 <= -8.5e+19) || !(z <= 2.7e-29))
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y * Float64(x_m / Float64(t - z)));
	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 <= -8.5e+19) || ~((z <= 2.7e-29)))
		tmp = x_m * (1.0 - (y / z));
	else
		tmp = y * (x_m / (t - z));
	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, -8.5e+19], N[Not[LessEqual[z, 2.7e-29]], $MachinePrecision]], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e19 or 2.70000000000000023e-29 < z

   1. Initial program 74.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 63.9%

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

      1. mul-1-neg 63.9%

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

      2. associate-/l* 82.6%

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

      3. distribute-rgt-neg-in 82.6%

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

      4. div-sub 82.6%

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

      5. sub-neg 82.6%

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

      6. *-inverses 82.6%

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

      7. metadata-eval 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in x around 0 82.6%

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

   if -8.5e19 < z < 2.70000000000000023e-29

   1. Initial program 91.5%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

      1. clear-num 88.5%

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

      2. associate-/r/ 90.0%

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

   6. Applied egg-rr 90.0%

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

   7. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*r/ 80.7%

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

   9. Simplified 80.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+19} \lor \neg \left(z \leq 2.7 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+19} \lor \neg \left(z \leq 2.1 \cdot 10^{-29}\right):\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -8.6e+19) (not (<= z 2.1e-29)))
    (* x_m (- 1.0 (/ y z)))
    (* x_m (/ y (- 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) {
	double tmp;
	if ((z <= -8.6e+19) || !(z <= 2.1e-29)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = x_m * (y / (t - z));
	}
	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 <= (-8.6d+19)) .or. (.not. (z <= 2.1d-29))) then
        tmp = x_m * (1.0d0 - (y / z))
    else
        tmp = x_m * (y / (t - z))
    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 <= -8.6e+19) || !(z <= 2.1e-29)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = x_m * (y / (t - z));
	}
	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 <= -8.6e+19) or not (z <= 2.1e-29):
		tmp = x_m * (1.0 - (y / z))
	else:
		tmp = x_m * (y / (t - z))
	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 <= -8.6e+19) || !(z <= 2.1e-29))
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	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 <= -8.6e+19) || ~((z <= 2.1e-29)))
		tmp = x_m * (1.0 - (y / z));
	else
		tmp = x_m * (y / (t - z));
	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, -8.6e+19], N[Not[LessEqual[z, 2.1e-29]], $MachinePrecision]], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.6e19 or 2.09999999999999989e-29 < z

   1. Initial program 74.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 63.9%

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

      1. mul-1-neg 63.9%

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

      2. associate-/l* 82.6%

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

      3. distribute-rgt-neg-in 82.6%

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

      4. div-sub 82.6%

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

      5. sub-neg 82.6%

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

      6. *-inverses 82.6%

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

      7. metadata-eval 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in x around 0 82.6%

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

   if -8.6e19 < z < 2.09999999999999989e-29

   1. Initial program 91.5%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around inf 77.7%

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

      1. associate-/l* 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+19} \lor \neg \left(z \leq 2.1 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+15} \lor \neg \left(z \leq 2.45 \cdot 10^{-60}\right):\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x\_m}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2.25e+15) (not (<= z 2.45e-60)))
    (* x_m (- 1.0 (/ y z)))
    (* y (/ x_m 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 ((z <= -2.25e+15) || !(z <= 2.45e-60)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = y * (x_m / 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 ((z <= (-2.25d+15)) .or. (.not. (z <= 2.45d-60))) then
        tmp = x_m * (1.0d0 - (y / z))
    else
        tmp = y * (x_m / 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 ((z <= -2.25e+15) || !(z <= 2.45e-60)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = y * (x_m / 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 (z <= -2.25e+15) or not (z <= 2.45e-60):
		tmp = x_m * (1.0 - (y / z))
	else:
		tmp = y * (x_m / 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 ((z <= -2.25e+15) || !(z <= 2.45e-60))
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y * Float64(x_m / 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 ((z <= -2.25e+15) || ~((z <= 2.45e-60)))
		tmp = x_m * (1.0 - (y / z));
	else
		tmp = y * (x_m / 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[z, -2.25e+15], N[Not[LessEqual[z, 2.45e-60]], $MachinePrecision]], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e15 or 2.44999999999999994e-60 < z

   1. Initial program 74.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-/l* 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

      4. div-sub 82.3%

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

      5. sub-neg 82.3%

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

      6. *-inverses 82.3%

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

      7. metadata-eval 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in x around 0 82.3%

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

   if -2.25e15 < z < 2.44999999999999994e-60

   1. Initial program 91.3%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 68.7%

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

      1. associate-/l* 70.0%

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

   7. Simplified 70.0%

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

      1. *-commutative 70.0%

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

      2. div-inv 70.0%

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

      3. associate-*l* 71.6%

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

      4. associate-/r/ 71.6%

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

      5. clear-num 71.6%

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

   9. Applied egg-rr 71.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+15} \lor \neg \left(z \leq 2.45 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+15} \lor \neg \left(z \leq 6.4 \cdot 10^{+18}\right):\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x\_m}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (or (<= z -6.2e+15) (not (<= z 6.4e+18))) x_m (* y (/ x_m 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 ((z <= -6.2e+15) || !(z <= 6.4e+18)) {
		tmp = x_m;
	} else {
		tmp = y * (x_m / 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 ((z <= (-6.2d+15)) .or. (.not. (z <= 6.4d+18))) then
        tmp = x_m
    else
        tmp = y * (x_m / 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 ((z <= -6.2e+15) || !(z <= 6.4e+18)) {
		tmp = x_m;
	} else {
		tmp = y * (x_m / 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 (z <= -6.2e+15) or not (z <= 6.4e+18):
		tmp = x_m
	else:
		tmp = y * (x_m / 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 ((z <= -6.2e+15) || !(z <= 6.4e+18))
		tmp = x_m;
	else
		tmp = Float64(y * Float64(x_m / 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 ((z <= -6.2e+15) || ~((z <= 6.4e+18)))
		tmp = x_m;
	else
		tmp = y * (x_m / 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[z, -6.2e+15], N[Not[LessEqual[z, 6.4e+18]], $MachinePrecision]], x$95$m, N[(y * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e15 or 6.4e18 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 60.4%

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

   if -6.2e15 < z < 6.4e18

   1. Initial program 91.5%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around 0 65.1%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

      1. *-commutative 67.0%

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

      2. div-inv 66.9%

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

      3. associate-*l* 67.7%

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

      4. associate-/r/ 67.7%

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

      5. clear-num 67.7%

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

   9. Applied egg-rr 67.7%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+15} \lor \neg \left(z \leq 6.4 \cdot 10^{+18}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+16} \lor \neg \left(z \leq 4.6 \cdot 10^{+18}\right):\\ \;\;\;\;x\_m\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (or (<= z -6.5e+16) (not (<= z 4.6e+18))) x_m (* x_m (/ y 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 ((z <= -6.5e+16) || !(z <= 4.6e+18)) {
		tmp = x_m;
	} else {
		tmp = x_m * (y / 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 ((z <= (-6.5d+16)) .or. (.not. (z <= 4.6d+18))) then
        tmp = x_m
    else
        tmp = x_m * (y / 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 ((z <= -6.5e+16) || !(z <= 4.6e+18)) {
		tmp = x_m;
	} else {
		tmp = x_m * (y / 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 (z <= -6.5e+16) or not (z <= 4.6e+18):
		tmp = x_m
	else:
		tmp = x_m * (y / 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 ((z <= -6.5e+16) || !(z <= 4.6e+18))
		tmp = x_m;
	else
		tmp = Float64(x_m * Float64(y / 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 ((z <= -6.5e+16) || ~((z <= 4.6e+18)))
		tmp = x_m;
	else
		tmp = x_m * (y / 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[z, -6.5e+16], N[Not[LessEqual[z, 4.6e+18]], $MachinePrecision]], x$95$m, N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e16 or 4.6e18 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 60.4%

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

   if -6.5e16 < z < 4.6e18

   1. Initial program 91.5%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around 0 65.1%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+16} \lor \neg \left(z \leq 4.6 \cdot 10^{+18}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x\_m}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 3.5e-26)
    (/ x_m (/ (- t z) (- y z)))
    (* (- y z) (/ x_m (- 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) {
	double tmp;
	if (x_m <= 3.5e-26) {
		tmp = x_m / ((t - z) / (y - z));
	} else {
		tmp = (y - z) * (x_m / (t - z));
	}
	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 <= 3.5d-26) then
        tmp = x_m / ((t - z) / (y - z))
    else
        tmp = (y - z) * (x_m / (t - z))
    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 <= 3.5e-26) {
		tmp = x_m / ((t - z) / (y - z));
	} else {
		tmp = (y - z) * (x_m / (t - z));
	}
	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 <= 3.5e-26:
		tmp = x_m / ((t - z) / (y - z))
	else:
		tmp = (y - z) * (x_m / (t - z))
	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 <= 3.5e-26)
		tmp = Float64(x_m / Float64(Float64(t - z) / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x_m / Float64(t - z)));
	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 <= 3.5e-26)
		tmp = x_m / ((t - z) / (y - z));
	else
		tmp = (y - z) * (x_m / (t - z));
	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, 3.5e-26], N[(x$95$m / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 3.49999999999999985e-26

   1. Initial program 88.1%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   if 3.49999999999999985e-26 < x

   1. Initial program 65.4%

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

      1. associate-*r/ 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-/l* 98.2%

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

   6. Applied egg-rr 98.2%

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

Alternative 13: 96.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 4.4 \cdot 10^{-26}:\\ \;\;\;\;x\_m \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 4.4e-26)
    (* x_m (/ (- y z) (- t z)))
    (* (- y z) (/ x_m (- 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) {
	double tmp;
	if (x_m <= 4.4e-26) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (y - z) * (x_m / (t - z));
	}
	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 <= 4.4d-26) then
        tmp = x_m * ((y - z) / (t - z))
    else
        tmp = (y - z) * (x_m / (t - z))
    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 <= 4.4e-26) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (y - z) * (x_m / (t - z));
	}
	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 <= 4.4e-26:
		tmp = x_m * ((y - z) / (t - z))
	else:
		tmp = (y - z) * (x_m / (t - z))
	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 <= 4.4e-26)
		tmp = Float64(x_m * Float64(Float64(y - z) / Float64(t - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x_m / Float64(t - z)));
	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 <= 4.4e-26)
		tmp = x_m * ((y - z) / (t - z));
	else
		tmp = (y - z) * (x_m / (t - z));
	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, 4.4e-26], N[(x$95$m * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 4.4000000000000002e-26

   1. Initial program 88.1%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   if 4.4000000000000002e-26 < x

   1. Initial program 65.4%

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

      1. associate-*r/ 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-/l* 98.2%

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

   6. Applied egg-rr 98.2%

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

Alternative 14: 96.9% 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 #s(literal 1 binary64) 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 82.5%

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

   1. associate-/l* 95.2%

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

3. Simplified 95.2%

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

Alternative 15: 34.8% 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 #s(literal 1 binary64) 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 82.5%

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

   1. associate-/l* 95.2%

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

3. Simplified 95.2%

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

5. Taylor expanded in z around inf 33.3%

   \[\leadsto \color{blue}{x} \]
6. 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 2024096 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

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