Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.6s

Alternatives: 13

Speedup: 1.0×

• 34.5% 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-def 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: 61.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.34 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-266}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))) (t_3 (* z (- t))))
   (if (<= y -8.2e+39)
     t_2
     (if (<= y -6.5e-129)
       t_3
       (if (<= y -1.34e-188)
         t_1
         (if (<= y -3.2e-266)
           t_3
           (if (<= y 2.3e-180)
             t_1
             (if (<= y 9.5e-98)
               t_3
               (if (<= y 6.6e-56)
                 t_1
                 (if (<= y 3.15e-49) t_3 (if (<= y 1.2) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = z * -t;
	double tmp;
	if (y <= -8.2e+39) {
		tmp = t_2;
	} else if (y <= -6.5e-129) {
		tmp = t_3;
	} else if (y <= -1.34e-188) {
		tmp = t_1;
	} else if (y <= -3.2e-266) {
		tmp = t_3;
	} else if (y <= 2.3e-180) {
		tmp = t_1;
	} else if (y <= 9.5e-98) {
		tmp = t_3;
	} else if (y <= 6.6e-56) {
		tmp = t_1;
	} else if (y <= 3.15e-49) {
		tmp = t_3;
	} else if (y <= 1.2) {
		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 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    t_3 = z * -t
    if (y <= (-8.2d+39)) then
        tmp = t_2
    else if (y <= (-6.5d-129)) then
        tmp = t_3
    else if (y <= (-1.34d-188)) then
        tmp = t_1
    else if (y <= (-3.2d-266)) then
        tmp = t_3
    else if (y <= 2.3d-180) then
        tmp = t_1
    else if (y <= 9.5d-98) then
        tmp = t_3
    else if (y <= 6.6d-56) then
        tmp = t_1
    else if (y <= 3.15d-49) then
        tmp = t_3
    else if (y <= 1.2d0) 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 * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = z * -t;
	double tmp;
	if (y <= -8.2e+39) {
		tmp = t_2;
	} else if (y <= -6.5e-129) {
		tmp = t_3;
	} else if (y <= -1.34e-188) {
		tmp = t_1;
	} else if (y <= -3.2e-266) {
		tmp = t_3;
	} else if (y <= 2.3e-180) {
		tmp = t_1;
	} else if (y <= 9.5e-98) {
		tmp = t_3;
	} else if (y <= 6.6e-56) {
		tmp = t_1;
	} else if (y <= 3.15e-49) {
		tmp = t_3;
	} else if (y <= 1.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	t_3 = z * -t
	tmp = 0
	if y <= -8.2e+39:
		tmp = t_2
	elif y <= -6.5e-129:
		tmp = t_3
	elif y <= -1.34e-188:
		tmp = t_1
	elif y <= -3.2e-266:
		tmp = t_3
	elif y <= 2.3e-180:
		tmp = t_1
	elif y <= 9.5e-98:
		tmp = t_3
	elif y <= 6.6e-56:
		tmp = t_1
	elif y <= 3.15e-49:
		tmp = t_3
	elif y <= 1.2:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -8.2e+39)
		tmp = t_2;
	elseif (y <= -6.5e-129)
		tmp = t_3;
	elseif (y <= -1.34e-188)
		tmp = t_1;
	elseif (y <= -3.2e-266)
		tmp = t_3;
	elseif (y <= 2.3e-180)
		tmp = t_1;
	elseif (y <= 9.5e-98)
		tmp = t_3;
	elseif (y <= 6.6e-56)
		tmp = t_1;
	elseif (y <= 3.15e-49)
		tmp = t_3;
	elseif (y <= 1.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	t_3 = z * -t;
	tmp = 0.0;
	if (y <= -8.2e+39)
		tmp = t_2;
	elseif (y <= -6.5e-129)
		tmp = t_3;
	elseif (y <= -1.34e-188)
		tmp = t_1;
	elseif (y <= -3.2e-266)
		tmp = t_3;
	elseif (y <= 2.3e-180)
		tmp = t_1;
	elseif (y <= 9.5e-98)
		tmp = t_3;
	elseif (y <= 6.6e-56)
		tmp = t_1;
	elseif (y <= 3.15e-49)
		tmp = t_3;
	elseif (y <= 1.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -8.2e+39], t$95$2, If[LessEqual[y, -6.5e-129], t$95$3, If[LessEqual[y, -1.34e-188], t$95$1, If[LessEqual[y, -3.2e-266], t$95$3, If[LessEqual[y, 2.3e-180], t$95$1, If[LessEqual[y, 9.5e-98], t$95$3, If[LessEqual[y, 6.6e-56], t$95$1, If[LessEqual[y, 3.15e-49], t$95$3, If[LessEqual[y, 1.2], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.20000000000000008e39 or 1.19999999999999996 < 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 79.5%

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

      1. *-commutative 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in x around -inf 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

      4. sub-neg 73.9%

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

      5. metadata-eval 73.9%

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

      6. +-commutative 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in y around inf 79.5%

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

   if -8.20000000000000008e39 < y < -6.49999999999999952e-129 or -1.34e-188 < y < -3.2e-266 or 2.29999999999999996e-180 < y < 9.5000000000000001e-98 or 6.59999999999999967e-56 < y < 3.1499999999999998e-49

   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 82.5%

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

   4. Taylor expanded in y around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in x around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-rgt-neg-out 60.9%

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

   9. Simplified 60.9%

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

   if -6.49999999999999952e-129 < y < -1.34e-188 or -3.2e-266 < y < 2.29999999999999996e-180 or 9.5000000000000001e-98 < y < 6.59999999999999967e-56 or 3.1499999999999998e-49 < y < 1.19999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in x around inf 67.9%

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

      1. cancel-sign-sub-inv 67.9%

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

      2. metadata-eval 67.9%

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

      3. *-lft-identity 67.9%

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

      4. +-commutative 67.9%

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

   8. Simplified 67.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.34 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-266}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.2:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-139}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-255}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+84} \lor \neg \left(x \leq 1.2 \cdot 10^{+135}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (+ z 1.0))))
   (if (<= x -2.5e-102)
     t_2
     (if (<= x -2.6e-139)
       (* y t)
       (if (<= x 6.2e-292)
         t_1
         (if (<= x 4.3e-255)
           (* y t)
           (if (<= x 1.16e-93)
             t_1
             (if (or (<= x 4.1e+84) (not (<= x 1.2e+135)))
               t_2
               (* y (- x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (x <= -2.5e-102) {
		tmp = t_2;
	} else if (x <= -2.6e-139) {
		tmp = y * t;
	} else if (x <= 6.2e-292) {
		tmp = t_1;
	} else if (x <= 4.3e-255) {
		tmp = y * t;
	} else if (x <= 1.16e-93) {
		tmp = t_1;
	} else if ((x <= 4.1e+84) || !(x <= 1.2e+135)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x * (z + 1.0d0)
    if (x <= (-2.5d-102)) then
        tmp = t_2
    else if (x <= (-2.6d-139)) then
        tmp = y * t
    else if (x <= 6.2d-292) then
        tmp = t_1
    else if (x <= 4.3d-255) then
        tmp = y * t
    else if (x <= 1.16d-93) then
        tmp = t_1
    else if ((x <= 4.1d+84) .or. (.not. (x <= 1.2d+135))) then
        tmp = t_2
    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 t_2 = x * (z + 1.0);
	double tmp;
	if (x <= -2.5e-102) {
		tmp = t_2;
	} else if (x <= -2.6e-139) {
		tmp = y * t;
	} else if (x <= 6.2e-292) {
		tmp = t_1;
	} else if (x <= 4.3e-255) {
		tmp = y * t;
	} else if (x <= 1.16e-93) {
		tmp = t_1;
	} else if ((x <= 4.1e+84) || !(x <= 1.2e+135)) {
		tmp = t_2;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (z + 1.0)
	tmp = 0
	if x <= -2.5e-102:
		tmp = t_2
	elif x <= -2.6e-139:
		tmp = y * t
	elif x <= 6.2e-292:
		tmp = t_1
	elif x <= 4.3e-255:
		tmp = y * t
	elif x <= 1.16e-93:
		tmp = t_1
	elif (x <= 4.1e+84) or not (x <= 1.2e+135):
		tmp = t_2
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (x <= -2.5e-102)
		tmp = t_2;
	elseif (x <= -2.6e-139)
		tmp = Float64(y * t);
	elseif (x <= 6.2e-292)
		tmp = t_1;
	elseif (x <= 4.3e-255)
		tmp = Float64(y * t);
	elseif (x <= 1.16e-93)
		tmp = t_1;
	elseif ((x <= 4.1e+84) || !(x <= 1.2e+135))
		tmp = t_2;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (x <= -2.5e-102)
		tmp = t_2;
	elseif (x <= -2.6e-139)
		tmp = y * t;
	elseif (x <= 6.2e-292)
		tmp = t_1;
	elseif (x <= 4.3e-255)
		tmp = y * t;
	elseif (x <= 1.16e-93)
		tmp = t_1;
	elseif ((x <= 4.1e+84) || ~((x <= 1.2e+135)))
		tmp = t_2;
	else
		tmp = y * -x;
	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[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e-102], t$95$2, If[LessEqual[x, -2.6e-139], N[(y * t), $MachinePrecision], If[LessEqual[x, 6.2e-292], t$95$1, If[LessEqual[x, 4.3e-255], N[(y * t), $MachinePrecision], If[LessEqual[x, 1.16e-93], t$95$1, If[Or[LessEqual[x, 4.1e+84], N[Not[LessEqual[x, 1.2e+135]], $MachinePrecision]], t$95$2, N[(y * (-x)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.50000000000000013e-102 or 1.15999999999999998e-93 < x < 4.1000000000000003e84 or 1.19999999999999999e135 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in x around inf 55.1%

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

      1. cancel-sign-sub-inv 55.1%

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

      2. metadata-eval 55.1%

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

      3. *-lft-identity 55.1%

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

      4. +-commutative 55.1%

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

   8. Simplified 55.1%

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

   if -2.50000000000000013e-102 < x < -2.5999999999999998e-139 or 6.1999999999999999e-292 < x < 4.29999999999999989e-255

   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 72.2%

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

      1. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in x around -inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. sub-neg 72.2%

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

      5. metadata-eval 72.2%

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

      6. +-commutative 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in t around inf 61.7%

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

       1. *-commutative 61.7%

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

   11. Simplified 61.7%

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

   if -2.5999999999999998e-139 < x < 6.1999999999999999e-292 or 4.29999999999999989e-255 < x < 1.15999999999999998e-93

   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 96.6%

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

   4. Taylor expanded in y around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in x around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. distribute-rgt-neg-out 64.5%

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

   9. Simplified 64.5%

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

   if 4.1000000000000003e84 < x < 1.19999999999999999e135

   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 76.6%

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

      1. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in x around inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

   8. Simplified 60.4%

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

   9. Taylor expanded in y around inf 51.8%

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

       1. *-commutative 51.8%

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

       2. neg-mul-1 51.8%

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

       3. distribute-rgt-neg-in 51.8%

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

   11. Simplified 51.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-139}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-255}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+84} \lor \neg \left(x \leq 1.2 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -43000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-185}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+31}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* z (- t))))
   (if (<= z -4e+198)
     (* x (+ z 1.0))
     (if (<= z -43000000000.0)
       t_2
       (if (<= z 6e-267)
         t_1
         (if (<= z 1.36e-185)
           (* y t)
           (if (<= z 4.8e-159) t_1 (if (<= z 2.9e+31) (* y t) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * -t;
	double tmp;
	if (z <= -4e+198) {
		tmp = x * (z + 1.0);
	} else if (z <= -43000000000.0) {
		tmp = t_2;
	} else if (z <= 6e-267) {
		tmp = t_1;
	} else if (z <= 1.36e-185) {
		tmp = y * t;
	} else if (z <= 4.8e-159) {
		tmp = t_1;
	} else if (z <= 2.9e+31) {
		tmp = y * t;
	} 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 * (1.0d0 - y)
    t_2 = z * -t
    if (z <= (-4d+198)) then
        tmp = x * (z + 1.0d0)
    else if (z <= (-43000000000.0d0)) then
        tmp = t_2
    else if (z <= 6d-267) then
        tmp = t_1
    else if (z <= 1.36d-185) then
        tmp = y * t
    else if (z <= 4.8d-159) then
        tmp = t_1
    else if (z <= 2.9d+31) then
        tmp = y * t
    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 * (1.0 - y);
	double t_2 = z * -t;
	double tmp;
	if (z <= -4e+198) {
		tmp = x * (z + 1.0);
	} else if (z <= -43000000000.0) {
		tmp = t_2;
	} else if (z <= 6e-267) {
		tmp = t_1;
	} else if (z <= 1.36e-185) {
		tmp = y * t;
	} else if (z <= 4.8e-159) {
		tmp = t_1;
	} else if (z <= 2.9e+31) {
		tmp = y * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = z * -t
	tmp = 0
	if z <= -4e+198:
		tmp = x * (z + 1.0)
	elif z <= -43000000000.0:
		tmp = t_2
	elif z <= 6e-267:
		tmp = t_1
	elif z <= 1.36e-185:
		tmp = y * t
	elif z <= 4.8e-159:
		tmp = t_1
	elif z <= 2.9e+31:
		tmp = y * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -4e+198)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= -43000000000.0)
		tmp = t_2;
	elseif (z <= 6e-267)
		tmp = t_1;
	elseif (z <= 1.36e-185)
		tmp = Float64(y * t);
	elseif (z <= 4.8e-159)
		tmp = t_1;
	elseif (z <= 2.9e+31)
		tmp = Float64(y * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = z * -t;
	tmp = 0.0;
	if (z <= -4e+198)
		tmp = x * (z + 1.0);
	elseif (z <= -43000000000.0)
		tmp = t_2;
	elseif (z <= 6e-267)
		tmp = t_1;
	elseif (z <= 1.36e-185)
		tmp = y * t;
	elseif (z <= 4.8e-159)
		tmp = t_1;
	elseif (z <= 2.9e+31)
		tmp = y * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -4e+198], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -43000000000.0], t$95$2, If[LessEqual[z, 6e-267], t$95$1, If[LessEqual[z, 1.36e-185], N[(y * t), $MachinePrecision], If[LessEqual[z, 4.8e-159], t$95$1, If[LessEqual[z, 2.9e+31], N[(y * t), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.00000000000000007e198

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in x around inf 63.7%

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

      1. cancel-sign-sub-inv 63.7%

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

      2. metadata-eval 63.7%

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

      3. *-lft-identity 63.7%

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

      4. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   if -4.00000000000000007e198 < z < -4.3e10 or 2.9e31 < 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 66.4%

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

   4. Taylor expanded in y around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   6. Simplified 58.3%

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

   7. Taylor expanded in x around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. distribute-rgt-neg-out 58.2%

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

   9. Simplified 58.2%

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

   if -4.3e10 < z < 5.9999999999999999e-267 or 1.36e-185 < z < 4.79999999999999995e-159

   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 88.8%

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

      1. *-commutative 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

   8. Simplified 60.0%

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

   if 5.9999999999999999e-267 < z < 1.36e-185 or 4.79999999999999995e-159 < z < 2.9e31

   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 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in x around -inf 88.1%

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

      1. +-commutative 88.1%

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

      2. mul-1-neg 88.1%

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

      3. unsub-neg 88.1%

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

      4. sub-neg 88.1%

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

      5. metadata-eval 88.1%

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

      6. +-commutative 88.1%

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

   8. Simplified 88.1%

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

   9. Taylor expanded in t around inf 60.3%

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

       1. *-commutative 60.3%

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

   11. Simplified 60.3%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -43000000000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-185}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+31}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ t_2 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{-255}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))) (t_2 (* x (+ (- z y) 1.0))))
   (if (<= x -1.5e-102)
     t_2
     (if (<= x -2.65e-139)
       (* y (- t x))
       (if (<= x 3.3e-292)
         t_1
         (if (<= x 4.05e-255) (+ x (* y t)) (if (<= x 3.2e-30) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -1.5e-102) {
		tmp = t_2;
	} else if (x <= -2.65e-139) {
		tmp = y * (t - x);
	} else if (x <= 3.3e-292) {
		tmp = t_1;
	} else if (x <= 4.05e-255) {
		tmp = x + (y * t);
	} else if (x <= 3.2e-30) {
		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 - (z * t)
    t_2 = x * ((z - y) + 1.0d0)
    if (x <= (-1.5d-102)) then
        tmp = t_2
    else if (x <= (-2.65d-139)) then
        tmp = y * (t - x)
    else if (x <= 3.3d-292) then
        tmp = t_1
    else if (x <= 4.05d-255) then
        tmp = x + (y * t)
    else if (x <= 3.2d-30) 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 - (z * t);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -1.5e-102) {
		tmp = t_2;
	} else if (x <= -2.65e-139) {
		tmp = y * (t - x);
	} else if (x <= 3.3e-292) {
		tmp = t_1;
	} else if (x <= 4.05e-255) {
		tmp = x + (y * t);
	} else if (x <= 3.2e-30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	t_2 = x * ((z - y) + 1.0)
	tmp = 0
	if x <= -1.5e-102:
		tmp = t_2
	elif x <= -2.65e-139:
		tmp = y * (t - x)
	elif x <= 3.3e-292:
		tmp = t_1
	elif x <= 4.05e-255:
		tmp = x + (y * t)
	elif x <= 3.2e-30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	t_2 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (x <= -1.5e-102)
		tmp = t_2;
	elseif (x <= -2.65e-139)
		tmp = Float64(y * Float64(t - x));
	elseif (x <= 3.3e-292)
		tmp = t_1;
	elseif (x <= 4.05e-255)
		tmp = Float64(x + Float64(y * t));
	elseif (x <= 3.2e-30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	t_2 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (x <= -1.5e-102)
		tmp = t_2;
	elseif (x <= -2.65e-139)
		tmp = y * (t - x);
	elseif (x <= 3.3e-292)
		tmp = t_1;
	elseif (x <= 4.05e-255)
		tmp = x + (y * t);
	elseif (x <= 3.2e-30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e-102], t$95$2, If[LessEqual[x, -2.65e-139], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-292], t$95$1, If[LessEqual[x, 4.05e-255], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-30], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.5e-102 or 3.2e-30 < 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 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

   5. Simplified 80.0%

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

   if -1.5e-102 < x < -2.6499999999999998e-139

   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 75.6%

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

      1. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around -inf 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. unsub-neg 75.7%

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

      4. sub-neg 75.7%

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

      5. metadata-eval 75.7%

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

      6. +-commutative 75.7%

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

   8. Simplified 75.7%

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

   9. Taylor expanded in y around inf 75.7%

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

   if -2.6499999999999998e-139 < x < 3.29999999999999995e-292 or 4.05e-255 < x < 3.2e-30

   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 94.9%

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

   4. Taylor expanded in y around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

   6. Simplified 70.7%

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

   if 3.29999999999999995e-292 < x < 4.05e-255

   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 82.1%

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

   4. Taylor expanded in z around 0 64.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-292}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{-255}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -175000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (* z (- t))))
   (if (<= z -2.3e+198)
     (* x (+ z 1.0))
     (if (<= z -175000000.0)
       t_2
       (if (<= z 2.25e-268)
         t_1
         (if (<= z 2.85e-164) (* y (- t x)) (if (<= z 9.5e+29) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = z * -t;
	double tmp;
	if (z <= -2.3e+198) {
		tmp = x * (z + 1.0);
	} else if (z <= -175000000.0) {
		tmp = t_2;
	} else if (z <= 2.25e-268) {
		tmp = t_1;
	} else if (z <= 2.85e-164) {
		tmp = y * (t - x);
	} else if (z <= 9.5e+29) {
		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)
    t_2 = z * -t
    if (z <= (-2.3d+198)) then
        tmp = x * (z + 1.0d0)
    else if (z <= (-175000000.0d0)) then
        tmp = t_2
    else if (z <= 2.25d-268) then
        tmp = t_1
    else if (z <= 2.85d-164) then
        tmp = y * (t - x)
    else if (z <= 9.5d+29) 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);
	double t_2 = z * -t;
	double tmp;
	if (z <= -2.3e+198) {
		tmp = x * (z + 1.0);
	} else if (z <= -175000000.0) {
		tmp = t_2;
	} else if (z <= 2.25e-268) {
		tmp = t_1;
	} else if (z <= 2.85e-164) {
		tmp = y * (t - x);
	} else if (z <= 9.5e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = z * -t
	tmp = 0
	if z <= -2.3e+198:
		tmp = x * (z + 1.0)
	elif z <= -175000000.0:
		tmp = t_2
	elif z <= 2.25e-268:
		tmp = t_1
	elif z <= 2.85e-164:
		tmp = y * (t - x)
	elif z <= 9.5e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2.3e+198)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= -175000000.0)
		tmp = t_2;
	elseif (z <= 2.25e-268)
		tmp = t_1;
	elseif (z <= 2.85e-164)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 9.5e+29)
		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);
	t_2 = z * -t;
	tmp = 0.0;
	if (z <= -2.3e+198)
		tmp = x * (z + 1.0);
	elseif (z <= -175000000.0)
		tmp = t_2;
	elseif (z <= 2.25e-268)
		tmp = t_1;
	elseif (z <= 2.85e-164)
		tmp = y * (t - x);
	elseif (z <= 9.5e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -2.3e+198], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -175000000.0], t$95$2, If[LessEqual[z, 2.25e-268], t$95$1, If[LessEqual[z, 2.85e-164], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+29], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3000000000000001e198

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in x around inf 63.7%

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

      1. cancel-sign-sub-inv 63.7%

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

      2. metadata-eval 63.7%

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

      3. *-lft-identity 63.7%

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

      4. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   if -2.3000000000000001e198 < z < -1.75e8 or 9.5000000000000003e29 < 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 66.4%

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

   4. Taylor expanded in y around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   6. Simplified 58.3%

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

   7. Taylor expanded in x around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. distribute-rgt-neg-out 58.2%

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

   9. Simplified 58.2%

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

   if -1.75e8 < z < 2.2500000000000001e-268 or 2.85000000000000011e-164 < z < 9.5000000000000003e29

   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 79.0%

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

   4. Taylor expanded in z around 0 69.1%

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

   if 2.2500000000000001e-268 < z < 2.85000000000000011e-164

   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 98.8%

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

      1. *-commutative 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in x around -inf 93.9%

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

      1. +-commutative 93.9%

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

      2. mul-1-neg 93.9%

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

      3. unsub-neg 93.9%

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

      4. sub-neg 93.9%

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

      5. metadata-eval 93.9%

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

      6. +-commutative 93.9%

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

   8. Simplified 93.9%

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

   9. Taylor expanded in y around inf 84.0%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -175000000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-268}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -7 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* z t))))
   (if (<= y -7e+39)
     t_1
     (if (<= y 3.5e-225)
       t_2
       (if (<= y 2.4e-185) (* x (+ z 1.0)) (if (<= y 5.7e-8) 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 <= -7e+39) {
		tmp = t_1;
	} else if (y <= 3.5e-225) {
		tmp = t_2;
	} else if (y <= 2.4e-185) {
		tmp = x * (z + 1.0);
	} else if (y <= 5.7e-8) {
		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 <= (-7d+39)) then
        tmp = t_1
    else if (y <= 3.5d-225) then
        tmp = t_2
    else if (y <= 2.4d-185) then
        tmp = x * (z + 1.0d0)
    else if (y <= 5.7d-8) 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 <= -7e+39) {
		tmp = t_1;
	} else if (y <= 3.5e-225) {
		tmp = t_2;
	} else if (y <= 2.4e-185) {
		tmp = x * (z + 1.0);
	} else if (y <= 5.7e-8) {
		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 <= -7e+39:
		tmp = t_1
	elif y <= 3.5e-225:
		tmp = t_2
	elif y <= 2.4e-185:
		tmp = x * (z + 1.0)
	elif y <= 5.7e-8:
		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 <= -7e+39)
		tmp = t_1;
	elseif (y <= 3.5e-225)
		tmp = t_2;
	elseif (y <= 2.4e-185)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 5.7e-8)
		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 <= -7e+39)
		tmp = t_1;
	elseif (y <= 3.5e-225)
		tmp = t_2;
	elseif (y <= 2.4e-185)
		tmp = x * (z + 1.0);
	elseif (y <= 5.7e-8)
		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, -7e+39], t$95$1, If[LessEqual[y, 3.5e-225], t$95$2, If[LessEqual[y, 2.4e-185], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.7e-8], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000003e39 or 5.70000000000000009e-8 < 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 78.8%

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

      1. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in x around -inf 73.2%

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

      1. +-commutative 73.2%

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

      2. mul-1-neg 73.2%

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

      3. unsub-neg 73.2%

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

      4. sub-neg 73.2%

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

      5. metadata-eval 73.2%

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

      6. +-commutative 73.2%

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

   8. Simplified 73.2%

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

   9. Taylor expanded in y around inf 78.9%

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

   if -7.0000000000000003e39 < y < 3.4999999999999997e-225 or 2.4000000000000001e-185 < y < 5.70000000000000009e-8

   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 79.7%

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

   4. Taylor expanded in y around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. unsub-neg 68.3%

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

   6. Simplified 68.3%

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

   if 3.4999999999999997e-225 < y < 2.4000000000000001e-185

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in x around inf 78.4%

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

      1. cancel-sign-sub-inv 78.4%

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

      2. metadata-eval 78.4%

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

      3. *-lft-identity 78.4%

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

      4. +-commutative 78.4%

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

   8. Simplified 78.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-74} \lor \neg \left(x \leq 3.2 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.2e-74) (not (<= x 3.2e+66)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.2e-74) || !(x <= 3.2e+66)) {
		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 <= (-1.2d-74)) .or. (.not. (x <= 3.2d+66))) 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 <= -1.2e-74) || !(x <= 3.2e+66)) {
		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 <= -1.2e-74) or not (x <= 3.2e+66):
		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 <= -1.2e-74) || !(x <= 3.2e+66))
		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 <= -1.2e-74) || ~((x <= 3.2e+66)))
		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, -1.2e-74], N[Not[LessEqual[x, 3.2e+66]], $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 < -1.1999999999999999e-74 or 3.2e66 < 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 84.3%

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

      1. mul-1-neg 84.3%

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

      2. unsub-neg 84.3%

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

   5. Simplified 84.3%

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

   if -1.1999999999999999e-74 < x < 3.2e66

   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 89.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-74} \lor \neg \left(x \leq 3.2 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5000 \lor \neg \left(z \leq 5.5 \cdot 10^{+29}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5000.0) (not (<= z 5.5e+29)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5000.0) || !(z <= 5.5e+29)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - 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 <= (-5000.0d0)) .or. (.not. (z <= 5.5d+29))) then
        tmp = x - (z * (t - x))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5000.0) || !(z <= 5.5e+29)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5000.0) or not (z <= 5.5e+29):
		tmp = x - (z * (t - x))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5000.0) || !(z <= 5.5e+29))
		tmp = Float64(x - Float64(z * Float64(t - x)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5000.0) || ~((z <= 5.5e+29)))
		tmp = x - (z * (t - x));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5000.0], N[Not[LessEqual[z, 5.5e+29]], $MachinePrecision]], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e3 or 5.5e29 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if -5e3 < z < 5.5e29

   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 89.9%

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

      1. *-commutative 89.9%

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

   5. Simplified 89.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5000 \lor \neg \left(z \leq 5.5 \cdot 10^{+29}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -180000000 \lor \neg \left(z \leq 6.6 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -180000000.0) (not (<= z 6.6e+29))) (* z (- t)) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -180000000.0) || !(z <= 6.6e+29)) {
		tmp = z * -t;
	} 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 ((z <= (-180000000.0d0)) .or. (.not. (z <= 6.6d+29))) then
        tmp = z * -t
    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 ((z <= -180000000.0) || !(z <= 6.6e+29)) {
		tmp = z * -t;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -180000000.0) or not (z <= 6.6e+29):
		tmp = z * -t
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -180000000.0) || !(z <= 6.6e+29))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -180000000.0) || ~((z <= 6.6e+29)))
		tmp = z * -t;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -180000000.0], N[Not[LessEqual[z, 6.6e+29]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e8 or 6.59999999999999968e29 < 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 59.7%

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

   4. Taylor expanded in y around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

   6. Simplified 54.4%

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

   7. Taylor expanded in x around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-rgt-neg-out 54.6%

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

   9. Simplified 54.6%

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

   if -1.8e8 < z < 6.59999999999999968e29

   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 88.5%

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

      1. *-commutative 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in x around -inf 86.0%

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

      1. +-commutative 86.0%

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

      2. mul-1-neg 86.0%

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

      3. unsub-neg 86.0%

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

      4. sub-neg 86.0%

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

      5. metadata-eval 86.0%

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

      6. +-commutative 86.0%

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

   8. Simplified 86.0%

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

   9. Taylor expanded in t around inf 41.0%

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

       1. *-commutative 41.0%

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

   11. Simplified 41.0%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -180000000 \lor \neg \left(z \leq 6.6 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-110} \lor \neg \left(y \leq 1.36 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.5e-110) (not (<= y 1.36e-18))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e-110) || !(y <= 1.36e-18)) {
		tmp = y * t;
	} 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 ((y <= (-5.5d-110)) .or. (.not. (y <= 1.36d-18))) then
        tmp = y * t
    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 ((y <= -5.5e-110) || !(y <= 1.36e-18)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.5e-110) or not (y <= 1.36e-18):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.5e-110) || !(y <= 1.36e-18))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.5e-110) || ~((y <= 1.36e-18)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.5e-110], N[Not[LessEqual[y, 1.36e-18]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999998e-110 or 1.3600000000000001e-18 < 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 68.5%

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

      1. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in x around -inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. sub-neg 64.1%

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

      5. metadata-eval 64.1%

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

      6. +-commutative 64.1%

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

   8. Simplified 64.1%

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

   9. Taylor expanded in t around inf 36.8%

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

       1. *-commutative 36.8%

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

   11. Simplified 36.8%

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

   if -5.4999999999999998e-110 < y < 1.3600000000000001e-18

   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 75.9%

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

   4. Taylor expanded in x around inf 27.0%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-110} \lor \neg \left(y \leq 1.36 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 13: 17.8% 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 67.3%

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

4. Taylor expanded in x around inf 14.7%

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

5. Final simplification 14.7%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 95.9% 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 2024020 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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