Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.5% → 98.9%

Time: 11.8s

Alternatives: 13

Speedup: 0.2×

• 21.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ t_2 := t\_1 \cdot x\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-308}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t\_1 \leq 10^{+280}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} + \frac{t \cdot x}{y \cdot \left(z + -1\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))) (t_2 (* t_1 x)))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 -1e-206)
       t_2
       (if (<= t_1 1e-308)
         (/ (+ y t) (/ z x))
         (if (<= t_1 1e+280)
           t_2
           (* y (+ (/ x z) (/ (* t x) (* y (+ z -1.0)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double t_2 = t_1 * x;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else if (t_1 <= -1e-206) {
		tmp = t_2;
	} else if (t_1 <= 1e-308) {
		tmp = (y + t) / (z / x);
	} else if (t_1 <= 1e+280) {
		tmp = t_2;
	} else {
		tmp = y * ((x / z) + ((t * x) / (y * (z + -1.0))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double t_2 = t_1 * x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else if (t_1 <= -1e-206) {
		tmp = t_2;
	} else if (t_1 <= 1e-308) {
		tmp = (y + t) / (z / x);
	} else if (t_1 <= 1e+280) {
		tmp = t_2;
	} else {
		tmp = y * ((x / z) + ((t * x) / (y * (z + -1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	t_2 = t_1 * x
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= -1e-206:
		tmp = t_2
	elif t_1 <= 1e-308:
		tmp = (y + t) / (z / x)
	elif t_1 <= 1e+280:
		tmp = t_2
	else:
		tmp = y * ((x / z) + ((t * x) / (y * (z + -1.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	t_2 = Float64(t_1 * x)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= -1e-206)
		tmp = t_2;
	elseif (t_1 <= 1e-308)
		tmp = Float64(Float64(y + t) / Float64(z / x));
	elseif (t_1 <= 1e+280)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(x / z) + Float64(Float64(t * x) / Float64(y * Float64(z + -1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	t_2 = t_1 * x;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= -1e-206)
		tmp = t_2;
	elseif (t_1 <= 1e-308)
		tmp = (y + t) / (z / x);
	elseif (t_1 <= 1e+280)
		tmp = t_2;
	else
		tmp = y * ((x / z) + ((t * x) / (y * (z + -1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * x), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-206], t$95$2, If[LessEqual[t$95$1, 1e-308], N[(N[(y + t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+280], t$95$2, N[(y * N[(N[(x / z), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -inf.0

   1. Initial program 42.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.9%

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

      1. mul-1-neg 91.9%

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

      2. distribute-neg-frac2 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

      4. neg-sub0 91.9%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 91.9%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in t around 0 99.6%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -1.00000000000000003e-206 or 9.9999999999999991e-309 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 1e280

   1. Initial program 99.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   if -1.00000000000000003e-206 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 9.9999999999999991e-309

   1. Initial program 74.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

      3. cancel-sign-sub-inv 99.8%

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

      4. metadata-eval 99.8%

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

      5. *-lft-identity 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.9%

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

      3. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

   if 1e280 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 72.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 99.9%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 99.9%

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t \cdot x}{y \cdot \left(-1 + z\right)} + \frac{x}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq -1 \cdot 10^{-206}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 10^{-308}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 10^{+280}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} + \frac{t \cdot x}{y \cdot \left(z + -1\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := \frac{y}{z} + \frac{t}{z + -1}\\ t_3 := t\_2 \cdot x\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-206}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-308}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t\_2 \leq 10^{+293}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))) (t_2 (+ (/ y z) (/ t (+ z -1.0)))) (t_3 (* t_2 x)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-206)
       t_3
       (if (<= t_2 1e-308)
         (/ (+ y t) (/ z x))
         (if (<= t_2 1e+293) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = (y / z) + (t / (z + -1.0));
	double t_3 = t_2 * x;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-206) {
		tmp = t_3;
	} else if (t_2 <= 1e-308) {
		tmp = (y + t) / (z / x);
	} else if (t_2 <= 1e+293) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = (y / z) + (t / (z + -1.0));
	double t_3 = t_2 * x;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-206) {
		tmp = t_3;
	} else if (t_2 <= 1e-308) {
		tmp = (y + t) / (z / x);
	} else if (t_2 <= 1e+293) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	t_2 = (y / z) + (t / (z + -1.0))
	t_3 = t_2 * x
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-206:
		tmp = t_3
	elif t_2 <= 1e-308:
		tmp = (y + t) / (z / x)
	elif t_2 <= 1e+293:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	t_2 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	t_3 = Float64(t_2 * x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-206)
		tmp = t_3;
	elseif (t_2 <= 1e-308)
		tmp = Float64(Float64(y + t) / Float64(z / x));
	elseif (t_2 <= 1e+293)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	t_2 = (y / z) + (t / (z + -1.0));
	t_3 = t_2 * x;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-206)
		tmp = t_3;
	elseif (t_2 <= 1e-308)
		tmp = (y + t) / (z / x);
	elseif (t_2 <= 1e+293)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-206], t$95$3, If[LessEqual[t$95$2, 1e-308], N[(N[(y + t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+293], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -inf.0 or 9.9999999999999992e292 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 56.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 96.5%

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

      1. mul-1-neg 96.5%

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

      2. distribute-neg-frac2 96.5%

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

      3. distribute-rgt-neg-in 96.5%

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

      4. neg-sub0 96.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 96.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in t around 0 99.8%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -1.00000000000000003e-206 or 9.9999999999999991e-309 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 9.9999999999999992e292

   1. Initial program 99.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   if -1.00000000000000003e-206 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 9.9999999999999991e-309

   1. Initial program 74.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

      3. cancel-sign-sub-inv 99.8%

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

      4. metadata-eval 99.8%

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

      5. *-lft-identity 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.9%

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

      3. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq -1 \cdot 10^{-206}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 10^{-308}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 10^{+293}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ t_2 := \frac{y}{z} \cdot x\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1650:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.25 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+260}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+283}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))) (t_2 (* (/ y z) x)))
   (if (<= z -1.9e+73)
     (/ (* y x) z)
     (if (<= z 1650.0)
       (* x (- (/ y z) t))
       (if (<= z 2.1e+41)
         t_1
         (if (<= z 4.25e+71)
           t_2
           (if (<= z 3.5e+131)
             (* x (/ t z))
             (if (<= z 5.2e+260)
               t_2
               (if (<= z 9e+283) t_1 (/ x (/ z y)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double t_2 = (y / z) * x;
	double tmp;
	if (z <= -1.9e+73) {
		tmp = (y * x) / z;
	} else if (z <= 1650.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 2.1e+41) {
		tmp = t_1;
	} else if (z <= 4.25e+71) {
		tmp = t_2;
	} else if (z <= 3.5e+131) {
		tmp = x * (t / z);
	} else if (z <= 5.2e+260) {
		tmp = t_2;
	} else if (z <= 9e+283) {
		tmp = t_1;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (x / z)
    t_2 = (y / z) * x
    if (z <= (-1.9d+73)) then
        tmp = (y * x) / z
    else if (z <= 1650.0d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 2.1d+41) then
        tmp = t_1
    else if (z <= 4.25d+71) then
        tmp = t_2
    else if (z <= 3.5d+131) then
        tmp = x * (t / z)
    else if (z <= 5.2d+260) then
        tmp = t_2
    else if (z <= 9d+283) then
        tmp = t_1
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double t_2 = (y / z) * x;
	double tmp;
	if (z <= -1.9e+73) {
		tmp = (y * x) / z;
	} else if (z <= 1650.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 2.1e+41) {
		tmp = t_1;
	} else if (z <= 4.25e+71) {
		tmp = t_2;
	} else if (z <= 3.5e+131) {
		tmp = x * (t / z);
	} else if (z <= 5.2e+260) {
		tmp = t_2;
	} else if (z <= 9e+283) {
		tmp = t_1;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	t_2 = (y / z) * x
	tmp = 0
	if z <= -1.9e+73:
		tmp = (y * x) / z
	elif z <= 1650.0:
		tmp = x * ((y / z) - t)
	elif z <= 2.1e+41:
		tmp = t_1
	elif z <= 4.25e+71:
		tmp = t_2
	elif z <= 3.5e+131:
		tmp = x * (t / z)
	elif z <= 5.2e+260:
		tmp = t_2
	elif z <= 9e+283:
		tmp = t_1
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	t_2 = Float64(Float64(y / z) * x)
	tmp = 0.0
	if (z <= -1.9e+73)
		tmp = Float64(Float64(y * x) / z);
	elseif (z <= 1650.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 2.1e+41)
		tmp = t_1;
	elseif (z <= 4.25e+71)
		tmp = t_2;
	elseif (z <= 3.5e+131)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= 5.2e+260)
		tmp = t_2;
	elseif (z <= 9e+283)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	t_2 = (y / z) * x;
	tmp = 0.0;
	if (z <= -1.9e+73)
		tmp = (y * x) / z;
	elseif (z <= 1650.0)
		tmp = x * ((y / z) - t);
	elseif (z <= 2.1e+41)
		tmp = t_1;
	elseif (z <= 4.25e+71)
		tmp = t_2;
	elseif (z <= 3.5e+131)
		tmp = x * (t / z);
	elseif (z <= 5.2e+260)
		tmp = t_2;
	elseif (z <= 9e+283)
		tmp = t_1;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.9e+73], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1650.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+41], t$95$1, If[LessEqual[z, 4.25e+71], t$95$2, If[LessEqual[z, 3.5e+131], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+260], t$95$2, If[LessEqual[z, 9e+283], t$95$1, N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.90000000000000011e73

   1. Initial program 95.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.2%

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

   if -1.90000000000000011e73 < z < 1650

   1. Initial program 90.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

      3. div-sub 86.4%

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

      4. associate-/l* 86.5%

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

      5. *-inverses 86.5%

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

      6. *-rgt-identity 86.5%

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

   5. Simplified 86.5%

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

   if 1650 < z < 2.1e41 or 5.1999999999999996e260 < z < 9.0000000000000002e283

   1. Initial program 89.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-neg-frac2 67.8%

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

      3. neg-sub0 67.8%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 67.8%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in z around inf 66.8%

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

      1. associate-/l* 77.5%

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

   8. Simplified 77.5%

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

   if 2.1e41 < z < 4.2499999999999998e71 or 3.4999999999999999e131 < z < 5.1999999999999996e260

   1. Initial program 97.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.3%

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

      1. associate-*r/ 72.3%

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

   5. Simplified 72.3%

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

   if 4.2499999999999998e71 < z < 3.4999999999999999e131

   1. Initial program 95.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-neg-frac2 82.9%

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

      3. neg-sub0 82.9%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 82.9%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in z around inf 82.9%

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

   if 9.0000000000000002e283 < z

   1. Initial program 99.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.4%

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

      1. associate-*r/ 81.4%

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

   5. Simplified 81.4%

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

      1. clear-num 81.4%

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

      2. un-div-inv 81.7%

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

   7. Applied egg-rr 81.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1650:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.25 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+260}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+283}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := \frac{y}{z} \cdot x\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-284}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+62}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))) (t_2 (* x (/ t z))) (t_3 (* (/ y z) x)))
   (if (<= t -6.8e+202)
     t_2
     (if (<= t -3e+145)
       t_1
       (if (<= t -1.2e+84)
         t_2
         (if (<= t -2e-284)
           t_3
           (if (<= t 2.35e-160) t_1 (if (<= t 6.2e+62) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = x * (t / z);
	double t_3 = (y / z) * x;
	double tmp;
	if (t <= -6.8e+202) {
		tmp = t_2;
	} else if (t <= -3e+145) {
		tmp = t_1;
	} else if (t <= -1.2e+84) {
		tmp = t_2;
	} else if (t <= -2e-284) {
		tmp = t_3;
	} else if (t <= 2.35e-160) {
		tmp = t_1;
	} else if (t <= 6.2e+62) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (x / z)
    t_2 = x * (t / z)
    t_3 = (y / z) * x
    if (t <= (-6.8d+202)) then
        tmp = t_2
    else if (t <= (-3d+145)) then
        tmp = t_1
    else if (t <= (-1.2d+84)) then
        tmp = t_2
    else if (t <= (-2d-284)) then
        tmp = t_3
    else if (t <= 2.35d-160) then
        tmp = t_1
    else if (t <= 6.2d+62) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = x * (t / z);
	double t_3 = (y / z) * x;
	double tmp;
	if (t <= -6.8e+202) {
		tmp = t_2;
	} else if (t <= -3e+145) {
		tmp = t_1;
	} else if (t <= -1.2e+84) {
		tmp = t_2;
	} else if (t <= -2e-284) {
		tmp = t_3;
	} else if (t <= 2.35e-160) {
		tmp = t_1;
	} else if (t <= 6.2e+62) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	t_2 = x * (t / z)
	t_3 = (y / z) * x
	tmp = 0
	if t <= -6.8e+202:
		tmp = t_2
	elif t <= -3e+145:
		tmp = t_1
	elif t <= -1.2e+84:
		tmp = t_2
	elif t <= -2e-284:
		tmp = t_3
	elif t <= 2.35e-160:
		tmp = t_1
	elif t <= 6.2e+62:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	t_2 = Float64(x * Float64(t / z))
	t_3 = Float64(Float64(y / z) * x)
	tmp = 0.0
	if (t <= -6.8e+202)
		tmp = t_2;
	elseif (t <= -3e+145)
		tmp = t_1;
	elseif (t <= -1.2e+84)
		tmp = t_2;
	elseif (t <= -2e-284)
		tmp = t_3;
	elseif (t <= 2.35e-160)
		tmp = t_1;
	elseif (t <= 6.2e+62)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	t_2 = x * (t / z);
	t_3 = (y / z) * x;
	tmp = 0.0;
	if (t <= -6.8e+202)
		tmp = t_2;
	elseif (t <= -3e+145)
		tmp = t_1;
	elseif (t <= -1.2e+84)
		tmp = t_2;
	elseif (t <= -2e-284)
		tmp = t_3;
	elseif (t <= 2.35e-160)
		tmp = t_1;
	elseif (t <= 6.2e+62)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -6.8e+202], t$95$2, If[LessEqual[t, -3e+145], t$95$1, If[LessEqual[t, -1.2e+84], t$95$2, If[LessEqual[t, -2e-284], t$95$3, If[LessEqual[t, 2.35e-160], t$95$1, If[LessEqual[t, 6.2e+62], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8e202 or -3.0000000000000002e145 < t < -1.2e84 or 6.20000000000000029e62 < t

   1. Initial program 94.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-neg-frac2 83.0%

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

      3. neg-sub0 83.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 83.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in z around inf 58.3%

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

   if -6.8e202 < t < -3.0000000000000002e145 or -2.00000000000000007e-284 < t < 2.3499999999999999e-160

   1. Initial program 82.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. distribute-neg-frac2 91.5%

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

      3. distribute-rgt-neg-in 91.5%

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

      4. neg-sub0 91.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 91.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around 0 89.4%

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

   if -1.2e84 < t < -2.00000000000000007e-284 or 2.3499999999999999e-160 < t < 6.20000000000000029e62

   1. Initial program 94.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.8%

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

      1. associate-*r/ 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-284}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-279}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* y (/ x z))))
   (if (<= t -5.6e+202)
     t_1
     (if (<= t -1.2e+146)
       t_2
       (if (<= t -1.06e+85)
         t_1
         (if (<= t -8.8e-279)
           (/ x (/ z y))
           (if (<= t 2.8e-155) t_2 (if (<= t 3.6e+59) (* (/ y z) x) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = y * (x / z);
	double tmp;
	if (t <= -5.6e+202) {
		tmp = t_1;
	} else if (t <= -1.2e+146) {
		tmp = t_2;
	} else if (t <= -1.06e+85) {
		tmp = t_1;
	} else if (t <= -8.8e-279) {
		tmp = x / (z / y);
	} else if (t <= 2.8e-155) {
		tmp = t_2;
	} else if (t <= 3.6e+59) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / z)
    t_2 = y * (x / z)
    if (t <= (-5.6d+202)) then
        tmp = t_1
    else if (t <= (-1.2d+146)) then
        tmp = t_2
    else if (t <= (-1.06d+85)) then
        tmp = t_1
    else if (t <= (-8.8d-279)) then
        tmp = x / (z / y)
    else if (t <= 2.8d-155) then
        tmp = t_2
    else if (t <= 3.6d+59) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = y * (x / z);
	double tmp;
	if (t <= -5.6e+202) {
		tmp = t_1;
	} else if (t <= -1.2e+146) {
		tmp = t_2;
	} else if (t <= -1.06e+85) {
		tmp = t_1;
	} else if (t <= -8.8e-279) {
		tmp = x / (z / y);
	} else if (t <= 2.8e-155) {
		tmp = t_2;
	} else if (t <= 3.6e+59) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = y * (x / z)
	tmp = 0
	if t <= -5.6e+202:
		tmp = t_1
	elif t <= -1.2e+146:
		tmp = t_2
	elif t <= -1.06e+85:
		tmp = t_1
	elif t <= -8.8e-279:
		tmp = x / (z / y)
	elif t <= 2.8e-155:
		tmp = t_2
	elif t <= 3.6e+59:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (t <= -5.6e+202)
		tmp = t_1;
	elseif (t <= -1.2e+146)
		tmp = t_2;
	elseif (t <= -1.06e+85)
		tmp = t_1;
	elseif (t <= -8.8e-279)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 2.8e-155)
		tmp = t_2;
	elseif (t <= 3.6e+59)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = y * (x / z);
	tmp = 0.0;
	if (t <= -5.6e+202)
		tmp = t_1;
	elseif (t <= -1.2e+146)
		tmp = t_2;
	elseif (t <= -1.06e+85)
		tmp = t_1;
	elseif (t <= -8.8e-279)
		tmp = x / (z / y);
	elseif (t <= 2.8e-155)
		tmp = t_2;
	elseif (t <= 3.6e+59)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+202], t$95$1, If[LessEqual[t, -1.2e+146], t$95$2, If[LessEqual[t, -1.06e+85], t$95$1, If[LessEqual[t, -8.8e-279], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-155], t$95$2, If[LessEqual[t, 3.6e+59], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.60000000000000032e202 or -1.2000000000000001e146 < t < -1.0600000000000001e85 or 3.5999999999999999e59 < t

   1. Initial program 94.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. distribute-neg-frac2 83.0%

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

      3. neg-sub0 83.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 83.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in z around inf 58.3%

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

   if -5.60000000000000032e202 < t < -1.2000000000000001e146 or -8.80000000000000002e-279 < t < 2.8e-155

   1. Initial program 82.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. distribute-neg-frac2 91.5%

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

      3. distribute-rgt-neg-in 91.5%

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

      4. neg-sub0 91.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 91.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around 0 89.4%

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

   if -1.0600000000000001e85 < t < -8.80000000000000002e-279

   1. Initial program 94.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.1%

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

      1. associate-*r/ 73.2%

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

   5. Simplified 73.2%

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

      1. clear-num 73.2%

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

      2. un-div-inv 73.3%

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

   7. Applied egg-rr 73.3%

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

   if 2.8e-155 < t < 3.5999999999999999e59

   1. Initial program 94.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.9%

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

      1. associate-*r/ 71.5%

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

   5. Simplified 71.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-279}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* y (/ x z))))
   (if (<= t -6.8e+202)
     t_1
     (if (<= t -3.2e+145)
       t_2
       (if (<= t -7.5e+87)
         (/ (* t x) z)
         (if (<= t -6.5e-282)
           (/ x (/ z y))
           (if (<= t 9e-160) t_2 (if (<= t 3e+61) (* (/ y z) x) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = y * (x / z);
	double tmp;
	if (t <= -6.8e+202) {
		tmp = t_1;
	} else if (t <= -3.2e+145) {
		tmp = t_2;
	} else if (t <= -7.5e+87) {
		tmp = (t * x) / z;
	} else if (t <= -6.5e-282) {
		tmp = x / (z / y);
	} else if (t <= 9e-160) {
		tmp = t_2;
	} else if (t <= 3e+61) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / z)
    t_2 = y * (x / z)
    if (t <= (-6.8d+202)) then
        tmp = t_1
    else if (t <= (-3.2d+145)) then
        tmp = t_2
    else if (t <= (-7.5d+87)) then
        tmp = (t * x) / z
    else if (t <= (-6.5d-282)) then
        tmp = x / (z / y)
    else if (t <= 9d-160) then
        tmp = t_2
    else if (t <= 3d+61) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = y * (x / z);
	double tmp;
	if (t <= -6.8e+202) {
		tmp = t_1;
	} else if (t <= -3.2e+145) {
		tmp = t_2;
	} else if (t <= -7.5e+87) {
		tmp = (t * x) / z;
	} else if (t <= -6.5e-282) {
		tmp = x / (z / y);
	} else if (t <= 9e-160) {
		tmp = t_2;
	} else if (t <= 3e+61) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = y * (x / z)
	tmp = 0
	if t <= -6.8e+202:
		tmp = t_1
	elif t <= -3.2e+145:
		tmp = t_2
	elif t <= -7.5e+87:
		tmp = (t * x) / z
	elif t <= -6.5e-282:
		tmp = x / (z / y)
	elif t <= 9e-160:
		tmp = t_2
	elif t <= 3e+61:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (t <= -6.8e+202)
		tmp = t_1;
	elseif (t <= -3.2e+145)
		tmp = t_2;
	elseif (t <= -7.5e+87)
		tmp = Float64(Float64(t * x) / z);
	elseif (t <= -6.5e-282)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 9e-160)
		tmp = t_2;
	elseif (t <= 3e+61)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = y * (x / z);
	tmp = 0.0;
	if (t <= -6.8e+202)
		tmp = t_1;
	elseif (t <= -3.2e+145)
		tmp = t_2;
	elseif (t <= -7.5e+87)
		tmp = (t * x) / z;
	elseif (t <= -6.5e-282)
		tmp = x / (z / y);
	elseif (t <= 9e-160)
		tmp = t_2;
	elseif (t <= 3e+61)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+202], t$95$1, If[LessEqual[t, -3.2e+145], t$95$2, If[LessEqual[t, -7.5e+87], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -6.5e-282], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-160], t$95$2, If[LessEqual[t, 3e+61], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.8e202 or 3e61 < t

   1. Initial program 94.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-neg-frac2 81.5%

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

      3. neg-sub0 81.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 81.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in z around inf 58.7%

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

   if -6.8e202 < t < -3.20000000000000008e145 or -6.50000000000000012e-282 < t < 9.00000000000000053e-160

   1. Initial program 82.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. distribute-neg-frac2 91.5%

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

      3. distribute-rgt-neg-in 91.5%

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

      4. neg-sub0 91.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 91.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around 0 89.4%

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

   if -3.20000000000000008e145 < t < -7.50000000000000014e87

   1. Initial program 99.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-neg-frac2 99.7%

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

      3. neg-sub0 99.7%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 99.7%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 54.5%

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

   if -7.50000000000000014e87 < t < -6.50000000000000012e-282

   1. Initial program 94.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.1%

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

      1. associate-*r/ 73.2%

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

   5. Simplified 73.2%

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

      1. clear-num 73.2%

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

      2. un-div-inv 73.3%

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

   7. Applied egg-rr 73.3%

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

   if 9.00000000000000053e-160 < t < 3e61

   1. Initial program 94.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.9%

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

      1. associate-*r/ 71.5%

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

   5. Simplified 71.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+64}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -5.4e+202)
     t_1
     (if (<= t -2.05e+142)
       (* y (/ x z))
       (if (<= t -2.4e+90)
         (/ (* t x) z)
         (if (<= t 1.55e+64) (/ (* y x) z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -5.4e+202) {
		tmp = t_1;
	} else if (t <= -2.05e+142) {
		tmp = y * (x / z);
	} else if (t <= -2.4e+90) {
		tmp = (t * x) / z;
	} else if (t <= 1.55e+64) {
		tmp = (y * x) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-5.4d+202)) then
        tmp = t_1
    else if (t <= (-2.05d+142)) then
        tmp = y * (x / z)
    else if (t <= (-2.4d+90)) then
        tmp = (t * x) / z
    else if (t <= 1.55d+64) then
        tmp = (y * x) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -5.4e+202) {
		tmp = t_1;
	} else if (t <= -2.05e+142) {
		tmp = y * (x / z);
	} else if (t <= -2.4e+90) {
		tmp = (t * x) / z;
	} else if (t <= 1.55e+64) {
		tmp = (y * x) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -5.4e+202:
		tmp = t_1
	elif t <= -2.05e+142:
		tmp = y * (x / z)
	elif t <= -2.4e+90:
		tmp = (t * x) / z
	elif t <= 1.55e+64:
		tmp = (y * x) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -5.4e+202)
		tmp = t_1;
	elseif (t <= -2.05e+142)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= -2.4e+90)
		tmp = Float64(Float64(t * x) / z);
	elseif (t <= 1.55e+64)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -5.4e+202)
		tmp = t_1;
	elseif (t <= -2.05e+142)
		tmp = y * (x / z);
	elseif (t <= -2.4e+90)
		tmp = (t * x) / z;
	elseif (t <= 1.55e+64)
		tmp = (y * x) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+202], t$95$1, If[LessEqual[t, -2.05e+142], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e+90], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.55e+64], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.3999999999999999e202 or 1.55e64 < t

   1. Initial program 94.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-neg-frac2 81.5%

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

      3. neg-sub0 81.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 81.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in z around inf 58.7%

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

   if -5.3999999999999999e202 < t < -2.04999999999999991e142

   1. Initial program 92.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-neg-frac2 75.0%

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

      3. distribute-rgt-neg-in 75.0%

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

      4. neg-sub0 75.0%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 75.0%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0 75.7%

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

   if -2.04999999999999991e142 < t < -2.4000000000000001e90

   1. Initial program 99.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-neg-frac2 99.7%

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

      3. neg-sub0 99.7%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 99.7%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around inf 54.5%

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

   if -2.4000000000000001e90 < t < 1.55e64

   1. Initial program 91.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+64}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-96} \lor \neg \left(y \leq 10^{-30}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-96) (not (<= y 1e-30)))
   (/ (* y x) z)
   (* x (/ t (+ z -1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-96) || !(y <= 1e-30)) {
		tmp = (y * x) / z;
	} else {
		tmp = x * (t / (z + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2d-96)) .or. (.not. (y <= 1d-30))) then
        tmp = (y * x) / z
    else
        tmp = x * (t / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-96) || !(y <= 1e-30)) {
		tmp = (y * x) / z;
	} else {
		tmp = x * (t / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-96) or not (y <= 1e-30):
		tmp = (y * x) / z
	else:
		tmp = x * (t / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-96) || !(y <= 1e-30))
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-96) || ~((y <= 1e-30)))
		tmp = (y * x) / z;
	else
		tmp = x * (t / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-96], N[Not[LessEqual[y, 1e-30]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999998e-96 or 1e-30 < y

   1. Initial program 89.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

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

   if -1.9999999999999998e-96 < y < 1e-30

   1. Initial program 96.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-neg-frac2 74.0%

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

      3. neg-sub0 74.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 74.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-96} \lor \neg \left(y \leq 10^{-30}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+26} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.7e+26) (not (<= z 0.048)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e+26) || !(z <= 0.048)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.7d+26)) .or. (.not. (z <= 0.048d0))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e+26) || !(z <= 0.048)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.7e+26) or not (z <= 0.048):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.7e+26) || !(z <= 0.048))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.7e+26) || ~((z <= 0.048)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.7e+26], N[Not[LessEqual[z, 0.048]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e26 or 0.048000000000000001 < z

   1. Initial program 95.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.0%

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

      1. *-commutative 90.0%

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

      2. remove-double-neg 90.0%

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

      3. cancel-sign-sub-inv 90.0%

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

      4. metadata-eval 90.0%

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

      5. *-lft-identity 90.0%

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

      6. distribute-neg-out 90.0%

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

      7. neg-mul-1 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-lft-neg-in 90.0%

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

      10. *-commutative 90.0%

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

      11. distribute-neg-frac 90.0%

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

      12. associate-/l* 95.5%

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

      13. distribute-rgt-neg-in 95.5%

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

      14. distribute-neg-frac 95.5%

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

   5. Simplified 95.5%

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

   if -2.7e26 < z < 0.048000000000000001

   1. Initial program 89.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

      3. div-sub 88.4%

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

      4. associate-/l* 88.4%

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

      5. *-inverses 88.4%

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

      6. *-rgt-identity 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+26} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+23) (not (<= z 0.048))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+23) || !(z <= 0.048)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d+23)) .or. (.not. (z <= 0.048d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+23) || !(z <= 0.048)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+23) or not (z <= 0.048):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+23) || !(z <= 0.048))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e+23) || ~((z <= 0.048)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+23], N[Not[LessEqual[z, 0.048]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999975e23 or 0.048000000000000001 < z

   1. Initial program 95.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-neg-frac2 54.1%

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

      3. neg-sub0 54.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 54.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in z around inf 50.0%

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

      1. associate-/l* 51.2%

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

   8. Simplified 51.2%

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

   if -3.79999999999999975e23 < z < 0.048000000000000001

   1. Initial program 89.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. distribute-neg-frac2 37.0%

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

      3. neg-sub0 37.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 37.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in z around 0 36.3%

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

      1. neg-mul-1 36.3%

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

   8. Simplified 36.3%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+23) (not (<= z 0.048))) (* x (/ t z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+23) || !(z <= 0.048)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d+23)) .or. (.not. (z <= 0.048d0))) then
        tmp = x * (t / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+23) || !(z <= 0.048)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+23) or not (z <= 0.048):
		tmp = x * (t / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+23) || !(z <= 0.048))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e+23) || ~((z <= 0.048)))
		tmp = x * (t / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+23], N[Not[LessEqual[z, 0.048]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999975e23 or 0.048000000000000001 < z

   1. Initial program 95.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-neg-frac2 54.1%

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

      3. neg-sub0 54.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 54.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in z around inf 54.1%

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

   if -3.79999999999999975e23 < z < 0.048000000000000001

   1. Initial program 89.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. distribute-neg-frac2 37.0%

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

      3. neg-sub0 37.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 37.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in z around 0 36.3%

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

      1. neg-mul-1 36.3%

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

   8. Simplified 36.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+23} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+202} \lor \neg \left(t \leq 7.2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6e+202) (not (<= t 7.2e+61))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6e+202) || !(t <= 7.2e+61)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6d+202)) .or. (.not. (t <= 7.2d+61))) then
        tmp = x * (t / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6e+202) || !(t <= 7.2e+61)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6e+202) or not (t <= 7.2e+61):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6e+202) || !(t <= 7.2e+61))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6e+202) || ~((t <= 7.2e+61)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6e+202], N[Not[LessEqual[t, 7.2e+61]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.0000000000000003e202 or 7.20000000000000021e61 < t

   1. Initial program 94.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-neg-frac2 81.5%

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

      3. neg-sub0 81.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 81.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in z around inf 58.7%

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

   if -6.0000000000000003e202 < t < 7.20000000000000021e61

   1. Initial program 91.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.4%

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

      1. associate-*r/ 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+202} \lor \neg \left(t \leq 7.2 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 23.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 46.0%

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

   1. mul-1-neg 46.0%

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

   2. distribute-neg-frac2 46.0%

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

   3. neg-sub0 46.0%

      \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

   4. associate--r- 46.0%

      \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

   5. metadata-eval 46.0%

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

5. Simplified 46.0%

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

6. Taylor expanded in z around 0 23.3%

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

   1. neg-mul-1 23.3%

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

8. Simplified 23.3%

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

9. Final simplification 23.3%

   \[\leadsto x \cdot \left(-t\right) \]
10. Add Preprocessing

Developer target: 94.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024054 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))