Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.1s

Alternatives: 14

Speedup: 1.0×

• 33.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, t - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right) \]
6. Add Preprocessing

Alternative 2: 38.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.00014:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+214}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -2.2e+52)
     (* y t)
     (if (<= y -7.5e-94)
       t_1
       (if (<= y -3.8e-215)
         x
         (if (<= y -5.5e-245)
           t_1
           (if (<= y 1.75e-208)
             x
             (if (<= y 5.6e-98)
               t_1
               (if (<= y 0.00014)
                 x
                 (if (<= y 8.2e+214) (* y t) (* y (- x))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -2.2e+52) {
		tmp = y * t;
	} else if (y <= -7.5e-94) {
		tmp = t_1;
	} else if (y <= -3.8e-215) {
		tmp = x;
	} else if (y <= -5.5e-245) {
		tmp = t_1;
	} else if (y <= 1.75e-208) {
		tmp = x;
	} else if (y <= 5.6e-98) {
		tmp = t_1;
	} else if (y <= 0.00014) {
		tmp = x;
	} else if (y <= 8.2e+214) {
		tmp = y * t;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-2.2d+52)) then
        tmp = y * t
    else if (y <= (-7.5d-94)) then
        tmp = t_1
    else if (y <= (-3.8d-215)) then
        tmp = x
    else if (y <= (-5.5d-245)) then
        tmp = t_1
    else if (y <= 1.75d-208) then
        tmp = x
    else if (y <= 5.6d-98) then
        tmp = t_1
    else if (y <= 0.00014d0) then
        tmp = x
    else if (y <= 8.2d+214) then
        tmp = y * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -2.2e+52) {
		tmp = y * t;
	} else if (y <= -7.5e-94) {
		tmp = t_1;
	} else if (y <= -3.8e-215) {
		tmp = x;
	} else if (y <= -5.5e-245) {
		tmp = t_1;
	} else if (y <= 1.75e-208) {
		tmp = x;
	} else if (y <= 5.6e-98) {
		tmp = t_1;
	} else if (y <= 0.00014) {
		tmp = x;
	} else if (y <= 8.2e+214) {
		tmp = y * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -2.2e+52:
		tmp = y * t
	elif y <= -7.5e-94:
		tmp = t_1
	elif y <= -3.8e-215:
		tmp = x
	elif y <= -5.5e-245:
		tmp = t_1
	elif y <= 1.75e-208:
		tmp = x
	elif y <= 5.6e-98:
		tmp = t_1
	elif y <= 0.00014:
		tmp = x
	elif y <= 8.2e+214:
		tmp = y * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -2.2e+52)
		tmp = Float64(y * t);
	elseif (y <= -7.5e-94)
		tmp = t_1;
	elseif (y <= -3.8e-215)
		tmp = x;
	elseif (y <= -5.5e-245)
		tmp = t_1;
	elseif (y <= 1.75e-208)
		tmp = x;
	elseif (y <= 5.6e-98)
		tmp = t_1;
	elseif (y <= 0.00014)
		tmp = x;
	elseif (y <= 8.2e+214)
		tmp = Float64(y * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -2.2e+52)
		tmp = y * t;
	elseif (y <= -7.5e-94)
		tmp = t_1;
	elseif (y <= -3.8e-215)
		tmp = x;
	elseif (y <= -5.5e-245)
		tmp = t_1;
	elseif (y <= 1.75e-208)
		tmp = x;
	elseif (y <= 5.6e-98)
		tmp = t_1;
	elseif (y <= 0.00014)
		tmp = x;
	elseif (y <= 8.2e+214)
		tmp = y * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -2.2e+52], N[(y * t), $MachinePrecision], If[LessEqual[y, -7.5e-94], t$95$1, If[LessEqual[y, -3.8e-215], x, If[LessEqual[y, -5.5e-245], t$95$1, If[LessEqual[y, 1.75e-208], x, If[LessEqual[y, 5.6e-98], t$95$1, If[LessEqual[y, 0.00014], x, If[LessEqual[y, 8.2e+214], N[(y * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2e52 or 1.3999999999999999e-4 < y < 8.2e214

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.9%

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

      1. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in y around inf 74.9%

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

   7. Taylor expanded in t around inf 46.5%

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

      1. *-commutative 46.5%

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

   9. Simplified 46.5%

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

   if -2.2e52 < y < -7.5000000000000003e-94 or -3.79999999999999977e-215 < y < -5.49999999999999962e-245 or 1.74999999999999996e-208 < y < 5.5999999999999998e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 71.1%

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

   4. Taylor expanded in y around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. *-commutative 64.4%

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

      3. distribute-rgt-neg-in 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in x around 0 52.8%

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

      1. associate-*r* 52.8%

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

      2. mul-1-neg 52.8%

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

   9. Simplified 52.8%

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

   if -7.5000000000000003e-94 < y < -3.79999999999999977e-215 or -5.49999999999999962e-245 < y < 1.74999999999999996e-208 or 5.5999999999999998e-98 < y < 1.3999999999999999e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.0%

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

   4. Taylor expanded in x around inf 57.2%

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

   if 8.2e214 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in y around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. distribute-lft-neg-out 74.1%

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

      3. *-commutative 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+52}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-245}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.00014:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+214}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(-t\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+91}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-186}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- t))) (t_3 (* x (- 1.0 y))))
   (if (<= z -4.5e+168)
     t_2
     (if (<= z -1.15e+91)
       (* z x)
       (if (<= z -2.8e-165)
         t_1
         (if (<= z -1.7e-186)
           t_3
           (if (<= z -6.6e-267)
             t_1
             (if (<= z 1.12e-14) t_3 (if (<= z 2.3e+182) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * -t;
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -4.5e+168) {
		tmp = t_2;
	} else if (z <= -1.15e+91) {
		tmp = z * x;
	} else if (z <= -2.8e-165) {
		tmp = t_1;
	} else if (z <= -1.7e-186) {
		tmp = t_3;
	} else if (z <= -6.6e-267) {
		tmp = t_1;
	} else if (z <= 1.12e-14) {
		tmp = t_3;
	} else if (z <= 2.3e+182) {
		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) :: t_3
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * -t
    t_3 = x * (1.0d0 - y)
    if (z <= (-4.5d+168)) then
        tmp = t_2
    else if (z <= (-1.15d+91)) then
        tmp = z * x
    else if (z <= (-2.8d-165)) then
        tmp = t_1
    else if (z <= (-1.7d-186)) then
        tmp = t_3
    else if (z <= (-6.6d-267)) then
        tmp = t_1
    else if (z <= 1.12d-14) then
        tmp = t_3
    else if (z <= 2.3d+182) 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 = y * (t - x);
	double t_2 = z * -t;
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -4.5e+168) {
		tmp = t_2;
	} else if (z <= -1.15e+91) {
		tmp = z * x;
	} else if (z <= -2.8e-165) {
		tmp = t_1;
	} else if (z <= -1.7e-186) {
		tmp = t_3;
	} else if (z <= -6.6e-267) {
		tmp = t_1;
	} else if (z <= 1.12e-14) {
		tmp = t_3;
	} else if (z <= 2.3e+182) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * -t
	t_3 = x * (1.0 - y)
	tmp = 0
	if z <= -4.5e+168:
		tmp = t_2
	elif z <= -1.15e+91:
		tmp = z * x
	elif z <= -2.8e-165:
		tmp = t_1
	elif z <= -1.7e-186:
		tmp = t_3
	elif z <= -6.6e-267:
		tmp = t_1
	elif z <= 1.12e-14:
		tmp = t_3
	elif z <= 2.3e+182:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(-t))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -4.5e+168)
		tmp = t_2;
	elseif (z <= -1.15e+91)
		tmp = Float64(z * x);
	elseif (z <= -2.8e-165)
		tmp = t_1;
	elseif (z <= -1.7e-186)
		tmp = t_3;
	elseif (z <= -6.6e-267)
		tmp = t_1;
	elseif (z <= 1.12e-14)
		tmp = t_3;
	elseif (z <= 2.3e+182)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * -t;
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -4.5e+168)
		tmp = t_2;
	elseif (z <= -1.15e+91)
		tmp = z * x;
	elseif (z <= -2.8e-165)
		tmp = t_1;
	elseif (z <= -1.7e-186)
		tmp = t_3;
	elseif (z <= -6.6e-267)
		tmp = t_1;
	elseif (z <= 1.12e-14)
		tmp = t_3;
	elseif (z <= 2.3e+182)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+168], t$95$2, If[LessEqual[z, -1.15e+91], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.8e-165], t$95$1, If[LessEqual[z, -1.7e-186], t$95$3, If[LessEqual[z, -6.6e-267], t$95$1, If[LessEqual[z, 1.12e-14], t$95$3, If[LessEqual[z, 2.3e+182], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.50000000000000012e168 or 2.3e182 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 66.9%

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

   4. Taylor expanded in y around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in x around 0 63.8%

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

      1. associate-*r* 63.8%

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

      2. mul-1-neg 63.8%

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

   9. Simplified 63.8%

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

   if -4.50000000000000012e168 < z < -1.14999999999999996e91

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.8%

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

      1. mul-1-neg 73.8%

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

      2. unsub-neg 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in z around inf 68.3%

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

   if -1.14999999999999996e91 < z < -2.7999999999999999e-165 or -1.7e-186 < z < -6.60000000000000007e-267 or 1.12000000000000006e-14 < z < 2.3e182

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in y around inf 74.7%

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

   7. Taylor expanded in y around inf 64.9%

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

   if -2.7999999999999999e-165 < z < -1.7e-186 or -6.60000000000000007e-267 < z < 1.12000000000000006e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in z around 0 76.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+91}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-267}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+89}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (- 1.0 y))))
   (if (<= z -3.4e+168)
     t_1
     (if (<= z -4.2e+89)
       (* z x)
       (if (<= z -8.8e-13)
         (* y t)
         (if (<= z -1.02e-115)
           t_2
           (if (<= z -7.8e-162) (* y t) (if (<= z 6.8e+106) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -3.4e+168) {
		tmp = t_1;
	} else if (z <= -4.2e+89) {
		tmp = z * x;
	} else if (z <= -8.8e-13) {
		tmp = y * t;
	} else if (z <= -1.02e-115) {
		tmp = t_2;
	} else if (z <= -7.8e-162) {
		tmp = y * t;
	} else if (z <= 6.8e+106) {
		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 = z * -t
    t_2 = x * (1.0d0 - y)
    if (z <= (-3.4d+168)) then
        tmp = t_1
    else if (z <= (-4.2d+89)) then
        tmp = z * x
    else if (z <= (-8.8d-13)) then
        tmp = y * t
    else if (z <= (-1.02d-115)) then
        tmp = t_2
    else if (z <= (-7.8d-162)) then
        tmp = y * t
    else if (z <= 6.8d+106) 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 = z * -t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -3.4e+168) {
		tmp = t_1;
	} else if (z <= -4.2e+89) {
		tmp = z * x;
	} else if (z <= -8.8e-13) {
		tmp = y * t;
	} else if (z <= -1.02e-115) {
		tmp = t_2;
	} else if (z <= -7.8e-162) {
		tmp = y * t;
	} else if (z <= 6.8e+106) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -3.4e+168:
		tmp = t_1
	elif z <= -4.2e+89:
		tmp = z * x
	elif z <= -8.8e-13:
		tmp = y * t
	elif z <= -1.02e-115:
		tmp = t_2
	elif z <= -7.8e-162:
		tmp = y * t
	elif z <= 6.8e+106:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -3.4e+168)
		tmp = t_1;
	elseif (z <= -4.2e+89)
		tmp = Float64(z * x);
	elseif (z <= -8.8e-13)
		tmp = Float64(y * t);
	elseif (z <= -1.02e-115)
		tmp = t_2;
	elseif (z <= -7.8e-162)
		tmp = Float64(y * t);
	elseif (z <= 6.8e+106)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -3.4e+168)
		tmp = t_1;
	elseif (z <= -4.2e+89)
		tmp = z * x;
	elseif (z <= -8.8e-13)
		tmp = y * t;
	elseif (z <= -1.02e-115)
		tmp = t_2;
	elseif (z <= -7.8e-162)
		tmp = y * t;
	elseif (z <= 6.8e+106)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+168], t$95$1, If[LessEqual[z, -4.2e+89], N[(z * x), $MachinePrecision], If[LessEqual[z, -8.8e-13], N[(y * t), $MachinePrecision], If[LessEqual[z, -1.02e-115], t$95$2, If[LessEqual[z, -7.8e-162], N[(y * t), $MachinePrecision], If[LessEqual[z, 6.8e+106], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000003e168 or 6.79999999999999989e106 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 66.1%

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

   4. Taylor expanded in y around 0 59.6%

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

      1. mul-1-neg 59.6%

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

      2. *-commutative 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in x around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. mul-1-neg 59.4%

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

   9. Simplified 59.4%

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

   if -3.40000000000000003e168 < z < -4.19999999999999972e89

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.8%

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

      1. mul-1-neg 73.8%

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

      2. unsub-neg 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in z around inf 68.3%

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

   if -4.19999999999999972e89 < z < -8.79999999999999986e-13 or -1.02e-115 < z < -7.7999999999999999e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.6%

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

      1. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in y around inf 73.6%

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

   7. Taylor expanded in t around inf 60.1%

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

      1. *-commutative 60.1%

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

   9. Simplified 60.1%

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

   if -8.79999999999999986e-13 < z < -1.02e-115 or -7.7999999999999999e-162 < z < 6.79999999999999989e106

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in z around 0 65.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+89}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-175}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+214}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1500.0)
   (* y t)
   (if (<= y 6e-200)
     x
     (if (<= y 2.3e-175)
       (* z x)
       (if (<= y 4.6e-6) x (if (<= y 1.08e+214) (* y t) (* y (- x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * t;
	} else if (y <= 6e-200) {
		tmp = x;
	} else if (y <= 2.3e-175) {
		tmp = z * x;
	} else if (y <= 4.6e-6) {
		tmp = x;
	} else if (y <= 1.08e+214) {
		tmp = y * t;
	} else {
		tmp = 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 (y <= (-1500.0d0)) then
        tmp = y * t
    else if (y <= 6d-200) then
        tmp = x
    else if (y <= 2.3d-175) then
        tmp = z * x
    else if (y <= 4.6d-6) then
        tmp = x
    else if (y <= 1.08d+214) then
        tmp = y * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * t;
	} else if (y <= 6e-200) {
		tmp = x;
	} else if (y <= 2.3e-175) {
		tmp = z * x;
	} else if (y <= 4.6e-6) {
		tmp = x;
	} else if (y <= 1.08e+214) {
		tmp = y * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1500.0:
		tmp = y * t
	elif y <= 6e-200:
		tmp = x
	elif y <= 2.3e-175:
		tmp = z * x
	elif y <= 4.6e-6:
		tmp = x
	elif y <= 1.08e+214:
		tmp = y * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1500.0)
		tmp = Float64(y * t);
	elseif (y <= 6e-200)
		tmp = x;
	elseif (y <= 2.3e-175)
		tmp = Float64(z * x);
	elseif (y <= 4.6e-6)
		tmp = x;
	elseif (y <= 1.08e+214)
		tmp = Float64(y * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1500.0)
		tmp = y * t;
	elseif (y <= 6e-200)
		tmp = x;
	elseif (y <= 2.3e-175)
		tmp = z * x;
	elseif (y <= 4.6e-6)
		tmp = x;
	elseif (y <= 1.08e+214)
		tmp = y * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1500.0], N[(y * t), $MachinePrecision], If[LessEqual[y, 6e-200], x, If[LessEqual[y, 2.3e-175], N[(z * x), $MachinePrecision], If[LessEqual[y, 4.6e-6], x, If[LessEqual[y, 1.08e+214], N[(y * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1500 or 4.6e-6 < y < 1.08e214

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in y around inf 73.7%

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

   7. Taylor expanded in t around inf 45.2%

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

      1. *-commutative 45.2%

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

   9. Simplified 45.2%

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

   if -1500 < y < 5.99999999999999989e-200 or 2.3e-175 < y < 4.6e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.0%

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

   4. Taylor expanded in x around inf 42.9%

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

   if 5.99999999999999989e-200 < y < 2.3e-175

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in z around inf 63.5%

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

   if 1.08e214 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in y around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. distribute-lft-neg-out 74.1%

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

      3. *-commutative 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-175}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+214}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + z \cdot x\\ \mathbf{if}\;y \leq -0.085:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.000115:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* z x))))
   (if (<= y -0.085)
     t_1
     (if (<= y 8.5e-137)
       t_2
       (if (<= y 5.8e-98) (* z (- t)) (if (<= y 0.000115) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x + (z * x);
	double tmp;
	if (y <= -0.085) {
		tmp = t_1;
	} else if (y <= 8.5e-137) {
		tmp = t_2;
	} else if (y <= 5.8e-98) {
		tmp = z * -t;
	} else if (y <= 0.000115) {
		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 = y * (t - x)
    t_2 = x + (z * x)
    if (y <= (-0.085d0)) then
        tmp = t_1
    else if (y <= 8.5d-137) then
        tmp = t_2
    else if (y <= 5.8d-98) then
        tmp = z * -t
    else if (y <= 0.000115d0) 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 = y * (t - x);
	double t_2 = x + (z * x);
	double tmp;
	if (y <= -0.085) {
		tmp = t_1;
	} else if (y <= 8.5e-137) {
		tmp = t_2;
	} else if (y <= 5.8e-98) {
		tmp = z * -t;
	} else if (y <= 0.000115) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + (z * x)
	tmp = 0
	if y <= -0.085:
		tmp = t_1
	elif y <= 8.5e-137:
		tmp = t_2
	elif y <= 5.8e-98:
		tmp = z * -t
	elif y <= 0.000115:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x + Float64(z * x))
	tmp = 0.0
	if (y <= -0.085)
		tmp = t_1;
	elseif (y <= 8.5e-137)
		tmp = t_2;
	elseif (y <= 5.8e-98)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 0.000115)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x + (z * x);
	tmp = 0.0;
	if (y <= -0.085)
		tmp = t_1;
	elseif (y <= 8.5e-137)
		tmp = t_2;
	elseif (y <= 5.8e-98)
		tmp = z * -t;
	elseif (y <= 0.000115)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.085], t$95$1, If[LessEqual[y, 8.5e-137], t$95$2, If[LessEqual[y, 5.8e-98], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 0.000115], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0850000000000000061 or 1.15e-4 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in y around inf 78.3%

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

   7. Taylor expanded in y around inf 77.4%

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

   if -0.0850000000000000061 < y < 8.5000000000000001e-137 or 5.8e-98 < y < 1.15e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-rgt-neg-in 66.3%

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

      3. neg-sub0 66.3%

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

      4. sub-neg 66.3%

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

      5. +-commutative 66.3%

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

      6. associate--r+ 66.3%

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

      7. neg-sub0 66.3%

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

      8. remove-double-neg 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in y around 0 65.0%

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

   if 8.5000000000000001e-137 < y < 5.8e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 80.7%

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

   4. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. *-commutative 63.9%

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

      3. distribute-rgt-neg-in 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in x around 0 64.1%

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

      1. associate-*r* 64.1%

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

      2. mul-1-neg 64.1%

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

   9. Simplified 64.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.085:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.000115:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -0.9:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.1:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -0.9)
     t_1
     (if (<= y 9.5e-137)
       (+ x (* z x))
       (if (<= y 1.6e-98) (* z (- t)) (if (<= y 0.1) (+ x (* y t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -0.9) {
		tmp = t_1;
	} else if (y <= 9.5e-137) {
		tmp = x + (z * x);
	} else if (y <= 1.6e-98) {
		tmp = z * -t;
	} else if (y <= 0.1) {
		tmp = x + (y * t);
	} 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 = y * (t - x)
    if (y <= (-0.9d0)) then
        tmp = t_1
    else if (y <= 9.5d-137) then
        tmp = x + (z * x)
    else if (y <= 1.6d-98) then
        tmp = z * -t
    else if (y <= 0.1d0) then
        tmp = x + (y * t)
    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 = y * (t - x);
	double tmp;
	if (y <= -0.9) {
		tmp = t_1;
	} else if (y <= 9.5e-137) {
		tmp = x + (z * x);
	} else if (y <= 1.6e-98) {
		tmp = z * -t;
	} else if (y <= 0.1) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -0.9:
		tmp = t_1
	elif y <= 9.5e-137:
		tmp = x + (z * x)
	elif y <= 1.6e-98:
		tmp = z * -t
	elif y <= 0.1:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -0.9)
		tmp = t_1;
	elseif (y <= 9.5e-137)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 1.6e-98)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 0.1)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -0.9)
		tmp = t_1;
	elseif (y <= 9.5e-137)
		tmp = x + (z * x);
	elseif (y <= 1.6e-98)
		tmp = z * -t;
	elseif (y <= 0.1)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.9], t$95$1, If[LessEqual[y, 9.5e-137], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-98], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 0.1], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.900000000000000022 or 0.10000000000000001 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.2%

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

      1. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around inf 78.2%

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

   7. Taylor expanded in y around inf 77.6%

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

   if -0.900000000000000022 < y < 9.5000000000000007e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. distribute-rgt-neg-in 65.4%

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

      3. neg-sub0 65.4%

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

      4. sub-neg 65.4%

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

      5. +-commutative 65.4%

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

      6. associate--r+ 65.4%

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

      7. neg-sub0 65.4%

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

      8. remove-double-neg 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in y around 0 64.7%

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

   if 9.5000000000000007e-137 < y < 1.6e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 80.7%

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

   4. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. *-commutative 63.9%

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

      3. distribute-rgt-neg-in 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in x around 0 64.1%

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

      1. associate-*r* 64.1%

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

      2. mul-1-neg 64.1%

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

   9. Simplified 64.1%

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

   if 1.6e-98 < y < 0.10000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 85.3%

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

   4. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.9:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.1:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -36000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-223}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 0.000135:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* z t))))
   (if (<= y -36000.0)
     t_1
     (if (<= y -1.7e-131)
       t_2
       (if (<= y -4.1e-223) (+ x (* z x)) (if (<= y 0.000135) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -36000.0) {
		tmp = t_1;
	} else if (y <= -1.7e-131) {
		tmp = t_2;
	} else if (y <= -4.1e-223) {
		tmp = x + (z * x);
	} else if (y <= 0.000135) {
		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 = y * (t - x)
    t_2 = x - (z * t)
    if (y <= (-36000.0d0)) then
        tmp = t_1
    else if (y <= (-1.7d-131)) then
        tmp = t_2
    else if (y <= (-4.1d-223)) then
        tmp = x + (z * x)
    else if (y <= 0.000135d0) 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 = y * (t - x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -36000.0) {
		tmp = t_1;
	} else if (y <= -1.7e-131) {
		tmp = t_2;
	} else if (y <= -4.1e-223) {
		tmp = x + (z * x);
	} else if (y <= 0.000135) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x - (z * t)
	tmp = 0
	if y <= -36000.0:
		tmp = t_1
	elif y <= -1.7e-131:
		tmp = t_2
	elif y <= -4.1e-223:
		tmp = x + (z * x)
	elif y <= 0.000135:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -36000.0)
		tmp = t_1;
	elseif (y <= -1.7e-131)
		tmp = t_2;
	elseif (y <= -4.1e-223)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 0.000135)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x - (z * t);
	tmp = 0.0;
	if (y <= -36000.0)
		tmp = t_1;
	elseif (y <= -1.7e-131)
		tmp = t_2;
	elseif (y <= -4.1e-223)
		tmp = x + (z * x);
	elseif (y <= 0.000135)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -36000.0], t$95$1, If[LessEqual[y, -1.7e-131], t$95$2, If[LessEqual[y, -4.1e-223], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.000135], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -36000 or 1.35000000000000002e-4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.7%

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

      1. *-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in y around inf 78.7%

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

   7. Taylor expanded in y around inf 78.2%

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

   if -36000 < y < -1.69999999999999998e-131 or -4.10000000000000015e-223 < y < 1.35000000000000002e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.4%

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

   4. Taylor expanded in y around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. *-commutative 75.2%

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

      3. distribute-rgt-neg-in 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in x around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. sub-neg 75.2%

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

   9. Simplified 75.2%

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

   if -1.69999999999999998e-131 < y < -4.10000000000000015e-223

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-rgt-neg-in 83.1%

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

      3. neg-sub0 83.1%

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

      4. sub-neg 83.1%

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

      5. +-commutative 83.1%

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

      6. associate--r+ 83.1%

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

      7. neg-sub0 83.1%

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

      8. remove-double-neg 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in y around 0 83.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -36000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-223}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 0.000135:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-179}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1500.0)
   (* y t)
   (if (<= y 2.4e-200)
     x
     (if (<= y 7.5e-179) (* z x) (if (<= y 1.25e-6) x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * t;
	} else if (y <= 2.4e-200) {
		tmp = x;
	} else if (y <= 7.5e-179) {
		tmp = z * x;
	} else if (y <= 1.25e-6) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1500.0d0)) then
        tmp = y * t
    else if (y <= 2.4d-200) then
        tmp = x
    else if (y <= 7.5d-179) then
        tmp = z * x
    else if (y <= 1.25d-6) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1500.0) {
		tmp = y * t;
	} else if (y <= 2.4e-200) {
		tmp = x;
	} else if (y <= 7.5e-179) {
		tmp = z * x;
	} else if (y <= 1.25e-6) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1500.0:
		tmp = y * t
	elif y <= 2.4e-200:
		tmp = x
	elif y <= 7.5e-179:
		tmp = z * x
	elif y <= 1.25e-6:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1500.0)
		tmp = Float64(y * t);
	elseif (y <= 2.4e-200)
		tmp = x;
	elseif (y <= 7.5e-179)
		tmp = Float64(z * x);
	elseif (y <= 1.25e-6)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1500.0)
		tmp = y * t;
	elseif (y <= 2.4e-200)
		tmp = x;
	elseif (y <= 7.5e-179)
		tmp = z * x;
	elseif (y <= 1.25e-6)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1500.0], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.4e-200], x, If[LessEqual[y, 7.5e-179], N[(z * x), $MachinePrecision], If[LessEqual[y, 1.25e-6], x, N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1500 or 1.2500000000000001e-6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.2%

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

      1. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around inf 78.2%

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

   7. Taylor expanded in t around inf 46.5%

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

      1. *-commutative 46.5%

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

   9. Simplified 46.5%

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

   if -1500 < y < 2.40000000000000002e-200 or 7.4999999999999996e-179 < y < 1.2500000000000001e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.0%

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

   4. Taylor expanded in x around inf 42.9%

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

   if 2.40000000000000002e-200 < y < 7.4999999999999996e-179

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in z around inf 63.5%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-179}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+106} \lor \neg \left(x \leq 9 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.9e+106) (not (<= x 9e-34)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.9e+106) || !(x <= 9e-34)) {
		tmp = x * ((z - y) + 1.0);
	} 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 ((x <= (-2.9d+106)) .or. (.not. (x <= 9d-34))) then
        tmp = x * ((z - y) + 1.0d0)
    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 ((x <= -2.9e+106) || !(x <= 9e-34)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.9e+106) or not (x <= 9e-34):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.9e+106) || !(x <= 9e-34))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	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 ((x <= -2.9e+106) || ~((x <= 9e-34)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.9e+106], N[Not[LessEqual[x, 9e-34]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9000000000000002e106 or 9.00000000000000085e-34 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.8%

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

      1. mul-1-neg 87.8%

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

      2. unsub-neg 87.8%

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

   5. Simplified 87.8%

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

   if -2.9000000000000002e106 < x < 9.00000000000000085e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 87.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+106} \lor \neg \left(x \leq 9 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-34}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.35e+106)
   (* x (+ (- z y) 1.0))
   (if (<= x 9e-34) (+ x (* (- y z) t)) (+ x (* x (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e+106) {
		tmp = x * ((z - y) + 1.0);
	} else if (x <= 9e-34) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (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) :: tmp
    if (x <= (-2.35d+106)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (x <= 9d-34) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (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 <= -2.35e+106) {
		tmp = x * ((z - y) + 1.0);
	} else if (x <= 9e-34) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.35e+106:
		tmp = x * ((z - y) + 1.0)
	elif x <= 9e-34:
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.35e+106)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (x <= 9e-34)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.35e+106)
		tmp = x * ((z - y) + 1.0);
	elseif (x <= 9e-34)
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.35e+106], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-34], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.35000000000000012e106

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

   if -2.35000000000000012e106 < x < 9.00000000000000085e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 87.9%

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

   if 9.00000000000000085e-34 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. distribute-rgt-neg-in 87.2%

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

      3. neg-sub0 87.2%

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

      4. sub-neg 87.2%

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

      5. +-commutative 87.2%

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

      6. associate--r+ 87.2%

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

      7. neg-sub0 87.2%

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

      8. remove-double-neg 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-34}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-12} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e-12) (not (<= z 1.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e-12) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.5d-12)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e-12) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.5e-12) or not (z <= 1.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.5e-12) || !(z <= 1.0))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e-12) || ~((z <= 1.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.5e-12], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999995e-12 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. unsub-neg 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in z around inf 34.4%

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

   if -9.4999999999999995e-12 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.3%

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

   4. Taylor expanded in x around inf 37.6%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-12} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

   \[\leadsto x + \left(y - z\right) \cdot \left(t - x\right) \]
4. Add Preprocessing

Alternative 14: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 69.0%

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

4. Taylor expanded in x around inf 20.2%

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

5. Final simplification 20.2%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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