Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.1% → 97.1%

Time: 13.1s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. *-commutative 97.3%

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

   2. clear-num 97.2%

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

   3. un-div-inv 97.3%

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

4. Applied egg-rr 97.3%

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

5. Final simplification 97.3%

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

Alternative 2: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1600000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+39} \lor \neg \left(y \leq 8.5 \cdot 10^{+53}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -6e+40)
     t_2
     (if (<= y -1600000.0)
       t_1
       (if (<= y -1.2e-14)
         t_2
         (if (<= y 2.8e-91)
           (* x (/ t (- z y)))
           (if (or (<= y 8e+39) (not (<= y 8.5e+53))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -6e+40) {
		tmp = t_2;
	} else if (y <= -1600000.0) {
		tmp = t_1;
	} else if (y <= -1.2e-14) {
		tmp = t_2;
	} else if (y <= 2.8e-91) {
		tmp = x * (t / (z - y));
	} else if ((y <= 8e+39) || !(y <= 8.5e+53)) {
		tmp = t_2;
	} 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) * (t / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-6d+40)) then
        tmp = t_2
    else if (y <= (-1600000.0d0)) then
        tmp = t_1
    else if (y <= (-1.2d-14)) then
        tmp = t_2
    else if (y <= 2.8d-91) then
        tmp = x * (t / (z - y))
    else if ((y <= 8d+39) .or. (.not. (y <= 8.5d+53))) then
        tmp = t_2
    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) * (t / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -6e+40) {
		tmp = t_2;
	} else if (y <= -1600000.0) {
		tmp = t_1;
	} else if (y <= -1.2e-14) {
		tmp = t_2;
	} else if (y <= 2.8e-91) {
		tmp = x * (t / (z - y));
	} else if ((y <= 8e+39) || !(y <= 8.5e+53)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -6e+40:
		tmp = t_2
	elif y <= -1600000.0:
		tmp = t_1
	elif y <= -1.2e-14:
		tmp = t_2
	elif y <= 2.8e-91:
		tmp = x * (t / (z - y))
	elif (y <= 8e+39) or not (y <= 8.5e+53):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -6e+40)
		tmp = t_2;
	elseif (y <= -1600000.0)
		tmp = t_1;
	elseif (y <= -1.2e-14)
		tmp = t_2;
	elseif (y <= 2.8e-91)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif ((y <= 8e+39) || !(y <= 8.5e+53))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -6e+40)
		tmp = t_2;
	elseif (y <= -1600000.0)
		tmp = t_1;
	elseif (y <= -1.2e-14)
		tmp = t_2;
	elseif (y <= 2.8e-91)
		tmp = x * (t / (z - y));
	elseif ((y <= 8e+39) || ~((y <= 8.5e+53)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+40], t$95$2, If[LessEqual[y, -1600000.0], t$95$1, If[LessEqual[y, -1.2e-14], t$95$2, If[LessEqual[y, 2.8e-91], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8e+39], N[Not[LessEqual[y, 8.5e+53]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000004e40 or -1.6e6 < y < -1.2e-14 or 2.8e-91 < y < 7.99999999999999952e39 or 8.5000000000000002e53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. div-sub 77.7%

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

      3. sub-neg 77.7%

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

      4. *-inverses 77.7%

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

      5. metadata-eval 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. mul-1-neg 71.4%

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

      3. distribute-rgt-neg-out 71.4%

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

      4. associate-*r/ 77.8%

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

      5. *-commutative 77.8%

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

      6. distribute-rgt1-in 77.7%

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

      7. +-commutative 77.7%

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

      8. distribute-frac-neg 77.7%

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

      9. sub-neg 77.7%

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

      10. *-commutative 77.7%

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

   8. Simplified 77.7%

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

   if -6.0000000000000004e40 < y < -1.6e6 or 7.99999999999999952e39 < y < 8.5000000000000002e53

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. associate-/l* 87.0%

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

      2. associate-/r/ 83.1%

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

   5. Simplified 83.1%

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

   if -1.2e-14 < y < 2.8e-91

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-*r/ 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1600000:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+39} \lor \neg \left(y \leq 8.5 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6.1 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1150000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -6.1e+40)
     t_2
     (if (<= y -1150000.0)
       t_1
       (if (<= y -8.6e-10)
         t_2
         (if (<= y -7e-295)
           (* x (/ t (- z y)))
           (if (<= y 1.2e-22)
             (* t (/ x (- z y)))
             (if (<= y 1e+54) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -6.1e+40) {
		tmp = t_2;
	} else if (y <= -1150000.0) {
		tmp = t_1;
	} else if (y <= -8.6e-10) {
		tmp = t_2;
	} else if (y <= -7e-295) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.2e-22) {
		tmp = t * (x / (z - y));
	} else if (y <= 1e+54) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = (x - y) * (t / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-6.1d+40)) then
        tmp = t_2
    else if (y <= (-1150000.0d0)) then
        tmp = t_1
    else if (y <= (-8.6d-10)) then
        tmp = t_2
    else if (y <= (-7d-295)) then
        tmp = x * (t / (z - y))
    else if (y <= 1.2d-22) then
        tmp = t * (x / (z - y))
    else if (y <= 1d+54) then
        tmp = t_1
    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 = (x - y) * (t / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -6.1e+40) {
		tmp = t_2;
	} else if (y <= -1150000.0) {
		tmp = t_1;
	} else if (y <= -8.6e-10) {
		tmp = t_2;
	} else if (y <= -7e-295) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.2e-22) {
		tmp = t * (x / (z - y));
	} else if (y <= 1e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -6.1e+40:
		tmp = t_2
	elif y <= -1150000.0:
		tmp = t_1
	elif y <= -8.6e-10:
		tmp = t_2
	elif y <= -7e-295:
		tmp = x * (t / (z - y))
	elif y <= 1.2e-22:
		tmp = t * (x / (z - y))
	elif y <= 1e+54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -6.1e+40)
		tmp = t_2;
	elseif (y <= -1150000.0)
		tmp = t_1;
	elseif (y <= -8.6e-10)
		tmp = t_2;
	elseif (y <= -7e-295)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.2e-22)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 1e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -6.1e+40)
		tmp = t_2;
	elseif (y <= -1150000.0)
		tmp = t_1;
	elseif (y <= -8.6e-10)
		tmp = t_2;
	elseif (y <= -7e-295)
		tmp = x * (t / (z - y));
	elseif (y <= 1.2e-22)
		tmp = t * (x / (z - y));
	elseif (y <= 1e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.1e+40], t$95$2, If[LessEqual[y, -1150000.0], t$95$1, If[LessEqual[y, -8.6e-10], t$95$2, If[LessEqual[y, -7e-295], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-22], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+54], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.1e40 or -1.15e6 < y < -8.60000000000000029e-10 or 1.0000000000000001e54 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. div-sub 80.4%

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

      3. sub-neg 80.4%

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

      4. *-inverses 80.4%

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

      5. metadata-eval 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in x around 0 72.8%

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

      1. associate-*r/ 72.8%

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

      2. mul-1-neg 72.8%

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

      3. distribute-rgt-neg-out 72.8%

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

      4. associate-*r/ 80.4%

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

      5. *-commutative 80.4%

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

      6. distribute-rgt1-in 80.4%

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

      7. +-commutative 80.4%

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

      8. distribute-frac-neg 80.4%

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

      9. sub-neg 80.4%

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

      10. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   if -6.1e40 < y < -1.15e6 or 1.20000000000000001e-22 < y < 1.0000000000000001e54

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 68.9%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 71.0%

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

   5. Simplified 71.0%

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

   if -8.60000000000000029e-10 < y < -6.99999999999999977e-295

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-*r/ 78.3%

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

   5. Simplified 78.3%

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

   if -6.99999999999999977e-295 < y < 1.20000000000000001e-22

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 83.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1150000:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 10^{+54}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -28000:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq -10.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e+95)
   t
   (if (<= y -28000.0)
     (* y (/ (- t) z))
     (if (<= y -10.5)
       t
       (if (<= y -2.4e-82)
         (* x (/ (- t) y))
         (if (<= y 4.5e-53) (/ (* t x) z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+95) {
		tmp = t;
	} else if (y <= -28000.0) {
		tmp = y * (-t / z);
	} else if (y <= -10.5) {
		tmp = t;
	} else if (y <= -2.4e-82) {
		tmp = x * (-t / y);
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = 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 (y <= (-5d+95)) then
        tmp = t
    else if (y <= (-28000.0d0)) then
        tmp = y * (-t / z)
    else if (y <= (-10.5d0)) then
        tmp = t
    else if (y <= (-2.4d-82)) then
        tmp = x * (-t / y)
    else if (y <= 4.5d-53) then
        tmp = (t * x) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+95) {
		tmp = t;
	} else if (y <= -28000.0) {
		tmp = y * (-t / z);
	} else if (y <= -10.5) {
		tmp = t;
	} else if (y <= -2.4e-82) {
		tmp = x * (-t / y);
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e+95:
		tmp = t
	elif y <= -28000.0:
		tmp = y * (-t / z)
	elif y <= -10.5:
		tmp = t
	elif y <= -2.4e-82:
		tmp = x * (-t / y)
	elif y <= 4.5e-53:
		tmp = (t * x) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e+95)
		tmp = t;
	elseif (y <= -28000.0)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (y <= -10.5)
		tmp = t;
	elseif (y <= -2.4e-82)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 4.5e-53)
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e+95)
		tmp = t;
	elseif (y <= -28000.0)
		tmp = y * (-t / z);
	elseif (y <= -10.5)
		tmp = t;
	elseif (y <= -2.4e-82)
		tmp = x * (-t / y);
	elseif (y <= 4.5e-53)
		tmp = (t * x) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e+95], t, If[LessEqual[y, -28000.0], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -10.5], t, If[LessEqual[y, -2.4e-82], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-53], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.00000000000000025e95 or -28000 < y < -10.5 or 4.49999999999999985e-53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 60.0%

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

   if -5.00000000000000025e95 < y < -28000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 62.4%

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

      1. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in x around 0 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-neg-frac 50.5%

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

      3. *-commutative 50.5%

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

      4. distribute-lft-neg-out 50.5%

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

      5. associate-*r/ 47.1%

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

      6. distribute-lft-neg-out 47.1%

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

      7. distribute-rgt-neg-in 47.1%

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

      8. distribute-neg-frac 47.1%

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

   8. Simplified 47.1%

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

   if -10.5 < y < -2.40000000000000008e-82

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-*r/ 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in z around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. distribute-neg-frac 63.3%

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

   8. Simplified 63.3%

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

   if -2.40000000000000008e-82 < y < 4.49999999999999985e-53

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 71.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -28000:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq -10.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-118} \lor \neg \left(y \leq 9.5 \cdot 10^{-143}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -4.8e-24)
     t_1
     (if (<= y -1.12e-100)
       (* x (/ (- t) y))
       (if (or (<= y -1.4e-118) (not (<= y 9.5e-143))) t_1 (/ t (/ z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.8e-24) {
		tmp = t_1;
	} else if (y <= -1.12e-100) {
		tmp = x * (-t / y);
	} else if ((y <= -1.4e-118) || !(y <= 9.5e-143)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-4.8d-24)) then
        tmp = t_1
    else if (y <= (-1.12d-100)) then
        tmp = x * (-t / y)
    else if ((y <= (-1.4d-118)) .or. (.not. (y <= 9.5d-143))) then
        tmp = t_1
    else
        tmp = t / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.8e-24) {
		tmp = t_1;
	} else if (y <= -1.12e-100) {
		tmp = x * (-t / y);
	} else if ((y <= -1.4e-118) || !(y <= 9.5e-143)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -4.8e-24:
		tmp = t_1
	elif y <= -1.12e-100:
		tmp = x * (-t / y)
	elif (y <= -1.4e-118) or not (y <= 9.5e-143):
		tmp = t_1
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.8e-24)
		tmp = t_1;
	elseif (y <= -1.12e-100)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif ((y <= -1.4e-118) || !(y <= 9.5e-143))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.8e-24)
		tmp = t_1;
	elseif (y <= -1.12e-100)
		tmp = x * (-t / y);
	elseif ((y <= -1.4e-118) || ~((y <= 9.5e-143)))
		tmp = t_1;
	else
		tmp = t / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-24], t$95$1, If[LessEqual[y, -1.12e-100], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.4e-118], N[Not[LessEqual[y, 9.5e-143]], $MachinePrecision]], t$95$1, N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999996e-24 or -1.11999999999999996e-100 < y < -1.4e-118 or 9.4999999999999993e-143 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. div-sub 70.2%

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

      3. sub-neg 70.2%

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

      4. *-inverses 70.2%

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

      5. metadata-eval 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in x around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. mul-1-neg 64.9%

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

      3. distribute-rgt-neg-out 64.9%

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

      4. associate-*r/ 70.2%

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

      5. *-commutative 70.2%

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

      6. distribute-rgt1-in 70.2%

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

      7. +-commutative 70.2%

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

      8. distribute-frac-neg 70.2%

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

      9. sub-neg 70.2%

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

      10. *-commutative 70.2%

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

   8. Simplified 70.2%

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

   if -4.7999999999999996e-24 < y < -1.11999999999999996e-100

   1. Initial program 75.6%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*r/ 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. distribute-neg-frac 75.3%

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

   8. Simplified 75.3%

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

   if -1.4e-118 < y < 9.4999999999999993e-143

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-118} \lor \neg \left(y \leq 9.5 \cdot 10^{-143}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2600000:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e+94)
   t
   (if (<= y -2600000.0)
     (* t (/ (- y) z))
     (if (<= y -1.8e-82)
       (* x (/ (- t) y))
       (if (<= y 4.5e-53) (/ (* t x) z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+94) {
		tmp = t;
	} else if (y <= -2600000.0) {
		tmp = t * (-y / z);
	} else if (y <= -1.8e-82) {
		tmp = x * (-t / y);
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = 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 (y <= (-1.3d+94)) then
        tmp = t
    else if (y <= (-2600000.0d0)) then
        tmp = t * (-y / z)
    else if (y <= (-1.8d-82)) then
        tmp = x * (-t / y)
    else if (y <= 4.5d-53) then
        tmp = (t * x) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+94) {
		tmp = t;
	} else if (y <= -2600000.0) {
		tmp = t * (-y / z);
	} else if (y <= -1.8e-82) {
		tmp = x * (-t / y);
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+94:
		tmp = t
	elif y <= -2600000.0:
		tmp = t * (-y / z)
	elif y <= -1.8e-82:
		tmp = x * (-t / y)
	elif y <= 4.5e-53:
		tmp = (t * x) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+94)
		tmp = t;
	elseif (y <= -2600000.0)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= -1.8e-82)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 4.5e-53)
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e+94)
		tmp = t;
	elseif (y <= -2600000.0)
		tmp = t * (-y / z);
	elseif (y <= -1.8e-82)
		tmp = x * (-t / y);
	elseif (y <= 4.5e-53)
		tmp = (t * x) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+94], t, If[LessEqual[y, -2600000.0], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e-82], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-53], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e94 or 4.49999999999999985e-53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 59.7%

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

   if -1.3e94 < y < -2.6e6

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 71.4%

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

      1. neg-mul-1 71.4%

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

      2. distribute-neg-frac 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. distribute-neg-frac 50.6%

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

   8. Simplified 50.6%

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

   if -2.6e6 < y < -1.79999999999999999e-82

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*r/ 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac 60.4%

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

   8. Simplified 60.4%

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

   if -1.79999999999999999e-82 < y < 4.49999999999999985e-53

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 71.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2600000:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -250000:\\ \;\;\;\;\frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+93)
   t
   (if (<= y -250000.0)
     (/ t (/ (- z) y))
     (if (<= y -2.5e-82)
       (* x (/ (- t) y))
       (if (<= y 4.5e-53) (/ (* t x) z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+93) {
		tmp = t;
	} else if (y <= -250000.0) {
		tmp = t / (-z / y);
	} else if (y <= -2.5e-82) {
		tmp = x * (-t / y);
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = 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 (y <= (-7.5d+93)) then
        tmp = t
    else if (y <= (-250000.0d0)) then
        tmp = t / (-z / y)
    else if (y <= (-2.5d-82)) then
        tmp = x * (-t / y)
    else if (y <= 4.5d-53) then
        tmp = (t * x) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+93) {
		tmp = t;
	} else if (y <= -250000.0) {
		tmp = t / (-z / y);
	} else if (y <= -2.5e-82) {
		tmp = x * (-t / y);
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+93:
		tmp = t
	elif y <= -250000.0:
		tmp = t / (-z / y)
	elif y <= -2.5e-82:
		tmp = x * (-t / y)
	elif y <= 4.5e-53:
		tmp = (t * x) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+93)
		tmp = t;
	elseif (y <= -250000.0)
		tmp = Float64(t / Float64(Float64(-z) / y));
	elseif (y <= -2.5e-82)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 4.5e-53)
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e+93)
		tmp = t;
	elseif (y <= -250000.0)
		tmp = t / (-z / y);
	elseif (y <= -2.5e-82)
		tmp = x * (-t / y);
	elseif (y <= 4.5e-53)
		tmp = (t * x) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+93], t, If[LessEqual[y, -250000.0], N[(t / N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-82], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-53], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5000000000000002e93 or 4.49999999999999985e-53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 59.7%

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

   if -7.5000000000000002e93 < y < -2.5e5

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 62.4%

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

      1. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in x around 0 50.6%

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

      1. neg-mul-1 50.6%

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

      2. distribute-neg-frac 50.6%

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

   8. Simplified 50.6%

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

   if -2.5e5 < y < -2.4999999999999999e-82

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*r/ 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac 60.4%

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

   8. Simplified 60.4%

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

   if -2.4999999999999999e-82 < y < 4.49999999999999985e-53

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 71.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -250000:\\ \;\;\;\;\frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+168} \lor \neg \left(y \leq 1.3 \cdot 10^{+117}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e+168) (not (<= y 1.3e+117)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+168) || !(y <= 1.3e+117)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (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) :: tmp
    if ((y <= (-8d+168)) .or. (.not. (y <= 1.3d+117))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+168) || !(y <= 1.3e+117)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e+168) or not (y <= 1.3e+117):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e+168) || !(y <= 1.3e+117))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e+168) || ~((y <= 1.3e+117)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e+168], N[Not[LessEqual[y, 1.3e+117]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999995e168 or 1.3e117 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. div-sub 90.6%

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

      3. sub-neg 90.6%

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

      4. *-inverses 90.6%

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

      5. metadata-eval 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in x around 0 79.9%

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

      1. associate-*r/ 79.9%

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

      2. mul-1-neg 79.9%

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

      3. distribute-rgt-neg-out 79.9%

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

      4. associate-*r/ 90.6%

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

      5. *-commutative 90.6%

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

      6. distribute-rgt1-in 90.6%

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

      7. +-commutative 90.6%

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

      8. distribute-frac-neg 90.6%

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

      9. sub-neg 90.6%

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

      10. *-commutative 90.6%

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

   8. Simplified 90.6%

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

   if -7.9999999999999995e168 < y < 1.3e117

   1. Initial program 96.4%

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

      1. associate-/r/ 90.2%

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

   3. Simplified 90.2%

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

      1. clear-num 89.9%

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

      2. associate-/r/ 89.9%

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

      3. clear-num 90.8%

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

   6. Applied egg-rr 90.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+168} \lor \neg \left(y \leq 1.3 \cdot 10^{+117}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2e+86)
   (* t (/ x (- z y)))
   (if (<= x 3.7e+58) (* t (/ (- y) (- z y))) (/ t (/ (- z y) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e+86) {
		tmp = t * (x / (z - y));
	} else if (x <= 3.7e+58) {
		tmp = t * (-y / (z - y));
	} else {
		tmp = t / ((z - y) / 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 (x <= (-2d+86)) then
        tmp = t * (x / (z - y))
    else if (x <= 3.7d+58) then
        tmp = t * (-y / (z - y))
    else
        tmp = t / ((z - y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e+86) {
		tmp = t * (x / (z - y));
	} else if (x <= 3.7e+58) {
		tmp = t * (-y / (z - y));
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2e+86:
		tmp = t * (x / (z - y))
	elif x <= 3.7e+58:
		tmp = t * (-y / (z - y))
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2e+86)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= 3.7e+58)
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - y)));
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2e+86)
		tmp = t * (x / (z - y));
	elseif (x <= 3.7e+58)
		tmp = t * (-y / (z - y));
	else
		tmp = t / ((z - y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2e+86], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+58], N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e86

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 82.1%

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

   if -2e86 < x < 3.7000000000000002e58

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 78.6%

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

      1. neg-mul-1 78.6%

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

      2. distribute-neg-frac 78.6%

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

   5. Simplified 78.6%

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

   if 3.7000000000000002e58 < x

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. clear-num 96.3%

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

      3. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in x around inf 76.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+22} \lor \neg \left(y \leq 2.8 \cdot 10^{-91}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+22) (not (<= y 2.8e-91)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+22) || !(y <= 2.8e-91)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (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) :: tmp
    if ((y <= (-3.8d+22)) .or. (.not. (y <= 2.8d-91))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+22) || !(y <= 2.8e-91)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+22) or not (y <= 2.8e-91):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+22) || !(y <= 2.8e-91))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e+22) || ~((y <= 2.8e-91)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+22], N[Not[LessEqual[y, 2.8e-91]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000004e22 or 2.8e-91 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. div-sub 74.6%

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

      3. sub-neg 74.6%

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

      4. *-inverses 74.6%

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

      5. metadata-eval 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in x around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. mul-1-neg 68.4%

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

      3. distribute-rgt-neg-out 68.4%

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

      4. associate-*r/ 74.6%

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

      5. *-commutative 74.6%

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

      6. distribute-rgt1-in 74.6%

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

      7. +-commutative 74.6%

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

      8. distribute-frac-neg 74.6%

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

      9. sub-neg 74.6%

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

      10. *-commutative 74.6%

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

   8. Simplified 74.6%

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

   if -3.8000000000000004e22 < y < 2.8e-91

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*r/ 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+22} \lor \neg \left(y \leq 2.8 \cdot 10^{-91}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15500000000 \lor \neg \left(z \leq 1.95 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -15500000000.0) (not (<= z 1.95e+34)))
   (* t (/ (- x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -15500000000.0) || !(z <= 1.95e+34)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-15500000000.0d0)) .or. (.not. (z <= 1.95d+34))) then
        tmp = t * ((x - y) / z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -15500000000.0) || !(z <= 1.95e+34)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -15500000000.0) or not (z <= 1.95e+34):
		tmp = t * ((x - y) / z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -15500000000.0) || !(z <= 1.95e+34))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -15500000000.0) || ~((z <= 1.95e+34)))
		tmp = t * ((x - y) / z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -15500000000.0], N[Not[LessEqual[z, 1.95e+34]], $MachinePrecision]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e10 or 1.9500000000000001e34 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 78.4%

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

   if -1.55e10 < z < 1.9500000000000001e34

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. div-sub 73.8%

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

      3. sub-neg 73.8%

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

      4. *-inverses 73.8%

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

      5. metadata-eval 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in x around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. mul-1-neg 70.3%

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

      3. distribute-rgt-neg-out 70.3%

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

      4. associate-*r/ 73.8%

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

      5. *-commutative 73.8%

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

      6. distribute-rgt1-in 73.8%

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

      7. +-commutative 73.8%

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

      8. distribute-frac-neg 73.8%

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

      9. sub-neg 73.8%

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

      10. *-commutative 73.8%

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

   8. Simplified 73.8%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15500000000 \lor \neg \left(z \leq 1.95 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+86} \lor \neg \left(x \leq 6 \cdot 10^{+58}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.95e+86) (not (<= x 6e+58)))
   (* t (/ x (- z y)))
   (/ t (- 1.0 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e+86) || !(x <= 6e+58)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / (1.0 - (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) :: tmp
    if ((x <= (-1.95d+86)) .or. (.not. (x <= 6d+58))) then
        tmp = t * (x / (z - y))
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e+86) || !(x <= 6e+58)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.95e+86) or not (x <= 6e+58):
		tmp = t * (x / (z - y))
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.95e+86) || !(x <= 6e+58))
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.95e+86) || ~((x <= 6e+58)))
		tmp = t * (x / (z - y));
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.95e+86], N[Not[LessEqual[x, 6e+58]], $MachinePrecision]], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9500000000000001e86 or 6.0000000000000005e58 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 78.7%

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

   if -1.9500000000000001e86 < x < 6.0000000000000005e58

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 98.0%

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

      3. un-div-inv 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in x around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. neg-sub0 78.5%

         \[\leadsto \frac{t}{\color{blue}{0 - \frac{z - y}{y}}} \]

      3. div-sub 78.5%

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

      4. *-inverses 78.5%

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

      5. associate-+l- 78.5%

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

      6. neg-sub0 78.5%

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

      7. neg-mul-1 78.5%

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

      8. +-commutative 78.5%

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

      9. neg-mul-1 78.5%

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

      10. unsub-neg 78.5%

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

   7. Simplified 78.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+86} \lor \neg \left(x \leq 6 \cdot 10^{+58}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.05e+86)
   (* t (/ x (- z y)))
   (if (<= x 3.7e+58) (/ t (- 1.0 (/ z y))) (/ t (/ (- z y) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.05e+86) {
		tmp = t * (x / (z - y));
	} else if (x <= 3.7e+58) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = t / ((z - y) / 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 (x <= (-2.05d+86)) then
        tmp = t * (x / (z - y))
    else if (x <= 3.7d+58) then
        tmp = t / (1.0d0 - (z / y))
    else
        tmp = t / ((z - y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.05e+86) {
		tmp = t * (x / (z - y));
	} else if (x <= 3.7e+58) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.05e+86:
		tmp = t * (x / (z - y))
	elif x <= 3.7e+58:
		tmp = t / (1.0 - (z / y))
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.05e+86)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= 3.7e+58)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.05e+86)
		tmp = t * (x / (z - y));
	elseif (x <= 3.7e+58)
		tmp = t / (1.0 - (z / y));
	else
		tmp = t / ((z - y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.05e+86], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+58], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.05e86

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 82.1%

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

   if -2.05e86 < x < 3.7000000000000002e58

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 98.0%

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

      3. un-div-inv 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in x around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. neg-sub0 78.5%

         \[\leadsto \frac{t}{\color{blue}{0 - \frac{z - y}{y}}} \]

      3. div-sub 78.5%

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

      4. *-inverses 78.5%

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

      5. associate-+l- 78.5%

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

      6. neg-sub0 78.5%

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

      7. neg-mul-1 78.5%

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

      8. +-commutative 78.5%

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

      9. neg-mul-1 78.5%

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

      10. unsub-neg 78.5%

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

   7. Simplified 78.5%

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

   if 3.7000000000000002e58 < x

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. clear-num 96.3%

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

      3. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in x around inf 76.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e+22) t (if (<= y 1.3e-79) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+22) {
		tmp = t;
	} else if (y <= 1.3e-79) {
		tmp = x * (t / z);
	} else {
		tmp = 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 (y <= (-9d+22)) then
        tmp = t
    else if (y <= 1.3d-79) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+22) {
		tmp = t;
	} else if (y <= 1.3e-79) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e+22:
		tmp = t
	elif y <= 1.3e-79:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e+22)
		tmp = t;
	elseif (y <= 1.3e-79)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e+22)
		tmp = t;
	elseif (y <= 1.3e-79)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e+22], t, If[LessEqual[y, 1.3e-79], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999996e22 or 1.29999999999999997e-79 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 54.6%

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

   if -8.9999999999999996e22 < y < 1.29999999999999997e-79

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 65.9%

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

      1. associate-/l* 65.8%

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

      2. associate-/r/ 63.7%

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

   5. Simplified 63.7%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e+22) t (if (<= y 4.5e-53) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+22) {
		tmp = t;
	} else if (y <= 4.5e-53) {
		tmp = t * (x / z);
	} else {
		tmp = 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 (y <= (-5.2d+22)) then
        tmp = t
    else if (y <= 4.5d-53) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+22) {
		tmp = t;
	} else if (y <= 4.5e-53) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e+22:
		tmp = t
	elif y <= 4.5e-53:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e+22)
		tmp = t;
	elseif (y <= 4.5e-53)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e+22)
		tmp = t;
	elseif (y <= 4.5e-53)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e+22], t, If[LessEqual[y, 4.5e-53], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e22 or 4.49999999999999985e-53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 56.3%

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

   if -5.2e22 < y < 4.49999999999999985e-53

   1. Initial program 94.7%

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

   3. Taylor expanded in y around 0 64.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e+28) t (if (<= y 4e-53) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+28) {
		tmp = t;
	} else if (y <= 4e-53) {
		tmp = t / (z / x);
	} else {
		tmp = 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 (y <= (-1.2d+28)) then
        tmp = t
    else if (y <= 4d-53) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+28) {
		tmp = t;
	} else if (y <= 4e-53) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e+28:
		tmp = t
	elif y <= 4e-53:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e+28)
		tmp = t;
	elseif (y <= 4e-53)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e+28)
		tmp = t;
	elseif (y <= 4e-53)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e+28], t, If[LessEqual[y, 4e-53], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999991e28 or 4.00000000000000012e-53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 56.3%

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

   if -1.19999999999999991e28 < y < 4.00000000000000012e-53

   1. Initial program 94.7%

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

   3. Taylor expanded in y around 0 64.5%

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

      1. associate-/l* 64.4%

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

   5. Simplified 64.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e+27) t (if (<= y 4.5e-53) (/ (* t x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e+27) {
		tmp = t;
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = 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 (y <= (-3.1d+27)) then
        tmp = t
    else if (y <= 4.5d-53) then
        tmp = (t * x) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e+27) {
		tmp = t;
	} else if (y <= 4.5e-53) {
		tmp = (t * x) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.1e+27:
		tmp = t
	elif y <= 4.5e-53:
		tmp = (t * x) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.1e+27)
		tmp = t;
	elseif (y <= 4.5e-53)
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.1e+27)
		tmp = t;
	elseif (y <= 4.5e-53)
		tmp = (t * x) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.1e+27], t, If[LessEqual[y, 4.5e-53], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999996e27 or 4.49999999999999985e-53 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 56.3%

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

   if -3.09999999999999996e27 < y < 4.49999999999999985e-53

   1. Initial program 94.7%

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

   3. Taylor expanded in y around 0 64.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

3. Final simplification 97.3%

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

Alternative 19: 35.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 97.3%

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

3. Taylor expanded in y around inf 34.1%

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

4. Final simplification 34.1%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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