Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 12

Speedup: 1.0×

• 34.4% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 52.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + x \cdot z\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-226}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 80000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+205} \lor \neg \left(z \leq 8.6 \cdot 10^{+231}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* x z))) (t_3 (+ x (* y t))))
   (if (<= z -2e+14)
     t_2
     (if (<= z -1.1e-226)
       t_3
       (if (<= z 9e-244)
         t_1
         (if (<= z 3.2e-35)
           t_3
           (if (<= z 80000.0)
             t_1
             (if (or (<= z 9.5e+205) (not (<= z 8.6e+231)))
               (* z (- t))
               t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -2e+14) {
		tmp = t_2;
	} else if (z <= -1.1e-226) {
		tmp = t_3;
	} else if (z <= 9e-244) {
		tmp = t_1;
	} else if (z <= 3.2e-35) {
		tmp = t_3;
	} else if (z <= 80000.0) {
		tmp = t_1;
	} else if ((z <= 9.5e+205) || !(z <= 8.6e+231)) {
		tmp = z * -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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (x * z)
    t_3 = x + (y * t)
    if (z <= (-2d+14)) then
        tmp = t_2
    else if (z <= (-1.1d-226)) then
        tmp = t_3
    else if (z <= 9d-244) then
        tmp = t_1
    else if (z <= 3.2d-35) then
        tmp = t_3
    else if (z <= 80000.0d0) then
        tmp = t_1
    else if ((z <= 9.5d+205) .or. (.not. (z <= 8.6d+231))) then
        tmp = z * -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 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -2e+14) {
		tmp = t_2;
	} else if (z <= -1.1e-226) {
		tmp = t_3;
	} else if (z <= 9e-244) {
		tmp = t_1;
	} else if (z <= 3.2e-35) {
		tmp = t_3;
	} else if (z <= 80000.0) {
		tmp = t_1;
	} else if ((z <= 9.5e+205) || !(z <= 8.6e+231)) {
		tmp = z * -t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (x * z)
	t_3 = x + (y * t)
	tmp = 0
	if z <= -2e+14:
		tmp = t_2
	elif z <= -1.1e-226:
		tmp = t_3
	elif z <= 9e-244:
		tmp = t_1
	elif z <= 3.2e-35:
		tmp = t_3
	elif z <= 80000.0:
		tmp = t_1
	elif (z <= 9.5e+205) or not (z <= 8.6e+231):
		tmp = z * -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(x + Float64(x * z))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -2e+14)
		tmp = t_2;
	elseif (z <= -1.1e-226)
		tmp = t_3;
	elseif (z <= 9e-244)
		tmp = t_1;
	elseif (z <= 3.2e-35)
		tmp = t_3;
	elseif (z <= 80000.0)
		tmp = t_1;
	elseif ((z <= 9.5e+205) || !(z <= 8.6e+231))
		tmp = Float64(z * Float64(-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 = x + (x * z);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -2e+14)
		tmp = t_2;
	elseif (z <= -1.1e-226)
		tmp = t_3;
	elseif (z <= 9e-244)
		tmp = t_1;
	elseif (z <= 3.2e-35)
		tmp = t_3;
	elseif (z <= 80000.0)
		tmp = t_1;
	elseif ((z <= 9.5e+205) || ~((z <= 8.6e+231)))
		tmp = z * -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[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+14], t$95$2, If[LessEqual[z, -1.1e-226], t$95$3, If[LessEqual[z, 9e-244], t$95$1, If[LessEqual[z, 3.2e-35], t$95$3, If[LessEqual[z, 80000.0], t$95$1, If[Or[LessEqual[z, 9.5e+205], N[Not[LessEqual[z, 8.6e+231]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2e14 or 9.4999999999999997e205 < z < 8.59999999999999952e231

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. distribute-rgt-neg-in 85.5%

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

      3. sub-neg 85.5%

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

      4. +-commutative 85.5%

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

      5. distribute-neg-in 85.5%

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

      6. unsub-neg 85.5%

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

      7. remove-double-neg 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0 52.5%

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

   if -2e14 < z < -1.1e-226 or 9.0000000000000003e-244 < z < 3.1999999999999998e-35

   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 85.6%

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

   4. Taylor expanded in y around inf 76.6%

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

      1. *-commutative 76.6%

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

   6. Simplified 76.6%

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

   if -1.1e-226 < z < 9.0000000000000003e-244 or 3.1999999999999998e-35 < z < 8e4

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-define 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 79.3%

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

      1. neg-mul-1 79.3%

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

      2. unsub-neg 79.3%

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

   10. Simplified 79.3%

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

   if 8e4 < z < 9.4999999999999997e205 or 8.59999999999999952e231 < 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 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-in 83.5%

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

      3. sub-neg 83.5%

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

      4. +-commutative 83.5%

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

      5. distribute-neg-in 83.5%

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

      6. unsub-neg 83.5%

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

      7. remove-double-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in x around -inf 81.5%

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

      1. distribute-lft-out 81.5%

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

      2. mul-1-neg 81.5%

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

      3. *-commutative 81.5%

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

      4. fma-define 81.5%

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

      5. sub-neg 81.5%

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

      6. metadata-eval 81.5%

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

      7. +-commutative 81.5%

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

      8. mul-1-neg 81.5%

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

      9. unsub-neg 81.5%

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

   8. Simplified 81.5%

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

   9. Taylor expanded in t around inf 56.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+14}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-226}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 80000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+205} \lor \neg \left(z \leq 8.6 \cdot 10^{+231}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x + t \cdot \left(y - z\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-226}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-33}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+92}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* z (- x t))) (t_3 (+ x (* t (- y z)))))
   (if (<= z -1.12e+58)
     t_2
     (if (<= z -1e-226)
       t_3
       (if (<= z 1.02e-243)
         t_1
         (if (<= z 3.4e-33)
           t_3
           (if (<= z 6.8e-12) t_1 (if (<= z 2.4e+92) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = x + (t * (y - z));
	double tmp;
	if (z <= -1.12e+58) {
		tmp = t_2;
	} else if (z <= -1e-226) {
		tmp = t_3;
	} else if (z <= 1.02e-243) {
		tmp = t_1;
	} else if (z <= 3.4e-33) {
		tmp = t_3;
	} else if (z <= 6.8e-12) {
		tmp = t_1;
	} else if (z <= 2.4e+92) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = z * (x - t)
    t_3 = x + (t * (y - z))
    if (z <= (-1.12d+58)) then
        tmp = t_2
    else if (z <= (-1d-226)) then
        tmp = t_3
    else if (z <= 1.02d-243) then
        tmp = t_1
    else if (z <= 3.4d-33) then
        tmp = t_3
    else if (z <= 6.8d-12) then
        tmp = t_1
    else if (z <= 2.4d+92) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = x + (t * (y - z));
	double tmp;
	if (z <= -1.12e+58) {
		tmp = t_2;
	} else if (z <= -1e-226) {
		tmp = t_3;
	} else if (z <= 1.02e-243) {
		tmp = t_1;
	} else if (z <= 3.4e-33) {
		tmp = t_3;
	} else if (z <= 6.8e-12) {
		tmp = t_1;
	} else if (z <= 2.4e+92) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = z * (x - t)
	t_3 = x + (t * (y - z))
	tmp = 0
	if z <= -1.12e+58:
		tmp = t_2
	elif z <= -1e-226:
		tmp = t_3
	elif z <= 1.02e-243:
		tmp = t_1
	elif z <= 3.4e-33:
		tmp = t_3
	elif z <= 6.8e-12:
		tmp = t_1
	elif z <= 2.4e+92:
		tmp = t_3
	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(x - t))
	t_3 = Float64(x + Float64(t * Float64(y - z)))
	tmp = 0.0
	if (z <= -1.12e+58)
		tmp = t_2;
	elseif (z <= -1e-226)
		tmp = t_3;
	elseif (z <= 1.02e-243)
		tmp = t_1;
	elseif (z <= 3.4e-33)
		tmp = t_3;
	elseif (z <= 6.8e-12)
		tmp = t_1;
	elseif (z <= 2.4e+92)
		tmp = t_3;
	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 * (x - t);
	t_3 = x + (t * (y - z));
	tmp = 0.0;
	if (z <= -1.12e+58)
		tmp = t_2;
	elseif (z <= -1e-226)
		tmp = t_3;
	elseif (z <= 1.02e-243)
		tmp = t_1;
	elseif (z <= 3.4e-33)
		tmp = t_3;
	elseif (z <= 6.8e-12)
		tmp = t_1;
	elseif (z <= 2.4e+92)
		tmp = t_3;
	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 * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+58], t$95$2, If[LessEqual[z, -1e-226], t$95$3, If[LessEqual[z, 1.02e-243], t$95$1, If[LessEqual[z, 3.4e-33], t$95$3, If[LessEqual[z, 6.8e-12], t$95$1, If[LessEqual[z, 2.4e+92], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12e58 or 2.40000000000000005e92 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. distribute-rgt-neg-in 89.9%

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

      3. sub-neg 89.9%

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

      4. +-commutative 89.9%

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

      5. distribute-neg-in 89.9%

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

      6. unsub-neg 89.9%

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

      7. remove-double-neg 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in x around -inf 85.5%

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

      1. distribute-lft-out 85.5%

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

      2. mul-1-neg 85.5%

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

      3. *-commutative 85.5%

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

      4. fma-define 86.6%

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

      5. sub-neg 86.6%

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

      6. metadata-eval 86.6%

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

      7. +-commutative 86.6%

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

      8. mul-1-neg 86.6%

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

      9. unsub-neg 86.6%

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

   8. Simplified 86.6%

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

   9. Taylor expanded in z around inf 89.9%

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

       1. neg-mul-1 89.9%

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

       2. sub-neg 89.9%

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

   11. Simplified 89.9%

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

   if -1.12e58 < z < -9.99999999999999921e-227 or 1.01999999999999996e-243 < z < 3.4000000000000001e-33 or 6.8000000000000001e-12 < z < 2.40000000000000005e92

   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%

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

   if -9.99999999999999921e-227 < z < 1.01999999999999996e-243 or 3.4000000000000001e-33 < z < 6.8000000000000001e-12

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-define 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 81.3%

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

      1. neg-mul-1 81.3%

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

      2. unsub-neg 81.3%

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

   10. Simplified 81.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-226}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-33}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+92}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -0.0034:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-146}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 550000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+207} \lor \neg \left(z \leq 8.2 \cdot 10^{+231}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (* x (- 1.0 y))))
   (if (<= z -0.0034)
     t_1
     (if (<= z 1.45e-223)
       t_2
       (if (<= z 7.6e-146)
         (* y t)
         (if (<= z 550000.0)
           t_2
           (if (or (<= z 5e+207) (not (<= z 8.2e+231))) (* z (- t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -0.0034) {
		tmp = t_1;
	} else if (z <= 1.45e-223) {
		tmp = t_2;
	} else if (z <= 7.6e-146) {
		tmp = y * t;
	} else if (z <= 550000.0) {
		tmp = t_2;
	} else if ((z <= 5e+207) || !(z <= 8.2e+231)) {
		tmp = z * -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) :: t_2
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = x * (1.0d0 - y)
    if (z <= (-0.0034d0)) then
        tmp = t_1
    else if (z <= 1.45d-223) then
        tmp = t_2
    else if (z <= 7.6d-146) then
        tmp = y * t
    else if (z <= 550000.0d0) then
        tmp = t_2
    else if ((z <= 5d+207) .or. (.not. (z <= 8.2d+231))) then
        tmp = z * -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 = x + (x * z);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -0.0034) {
		tmp = t_1;
	} else if (z <= 1.45e-223) {
		tmp = t_2;
	} else if (z <= 7.6e-146) {
		tmp = y * t;
	} else if (z <= 550000.0) {
		tmp = t_2;
	} else if ((z <= 5e+207) || !(z <= 8.2e+231)) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -0.0034:
		tmp = t_1
	elif z <= 1.45e-223:
		tmp = t_2
	elif z <= 7.6e-146:
		tmp = y * t
	elif z <= 550000.0:
		tmp = t_2
	elif (z <= 5e+207) or not (z <= 8.2e+231):
		tmp = z * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -0.0034)
		tmp = t_1;
	elseif (z <= 1.45e-223)
		tmp = t_2;
	elseif (z <= 7.6e-146)
		tmp = Float64(y * t);
	elseif (z <= 550000.0)
		tmp = t_2;
	elseif ((z <= 5e+207) || !(z <= 8.2e+231))
		tmp = Float64(z * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -0.0034)
		tmp = t_1;
	elseif (z <= 1.45e-223)
		tmp = t_2;
	elseif (z <= 7.6e-146)
		tmp = y * t;
	elseif (z <= 550000.0)
		tmp = t_2;
	elseif ((z <= 5e+207) || ~((z <= 8.2e+231)))
		tmp = z * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0034], t$95$1, If[LessEqual[z, 1.45e-223], t$95$2, If[LessEqual[z, 7.6e-146], N[(y * t), $MachinePrecision], If[LessEqual[z, 550000.0], t$95$2, If[Or[LessEqual[z, 5e+207], N[Not[LessEqual[z, 8.2e+231]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.00339999999999999981 or 4.9999999999999999e207 < z < 8.2000000000000006e231

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

      3. sub-neg 83.4%

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

      4. +-commutative 83.4%

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

      5. distribute-neg-in 83.4%

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

      6. unsub-neg 83.4%

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

      7. remove-double-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in t around 0 51.8%

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

   if -0.00339999999999999981 < z < 1.45e-223 or 7.59999999999999989e-146 < z < 5.5e5

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-define 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 61.0%

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

      1. neg-mul-1 61.0%

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

      2. unsub-neg 61.0%

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

   10. Simplified 61.0%

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

   if 1.45e-223 < z < 7.59999999999999989e-146

   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 96.7%

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

      1. *-commutative 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   if 5.5e5 < z < 4.9999999999999999e207 or 8.2000000000000006e231 < 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 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-in 83.5%

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

      3. sub-neg 83.5%

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

      4. +-commutative 83.5%

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

      5. distribute-neg-in 83.5%

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

      6. unsub-neg 83.5%

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

      7. remove-double-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in x around -inf 81.5%

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

      1. distribute-lft-out 81.5%

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

      2. mul-1-neg 81.5%

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

      3. *-commutative 81.5%

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

      4. fma-define 81.5%

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

      5. sub-neg 81.5%

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

      6. metadata-eval 81.5%

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

      7. +-commutative 81.5%

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

      8. mul-1-neg 81.5%

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

      9. unsub-neg 81.5%

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

   8. Simplified 81.5%

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

   9. Taylor expanded in t around inf 56.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0034:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-146}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 550000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+207} \lor \neg \left(z \leq 8.2 \cdot 10^{+231}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;y \leq -1 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-135}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* y t))))
   (if (<= y -1e+257)
     t_1
     (if (<= y -1.4e+45)
       t_2
       (if (<= y -1.1e-135)
         (+ x (* x z))
         (if (<= y 1.5e-39)
           (- x (* z t))
           (if (<= y 1.45e+242) t_2 (if (<= y 3.5e+301) t_1 (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (y * t);
	double tmp;
	if (y <= -1e+257) {
		tmp = t_1;
	} else if (y <= -1.4e+45) {
		tmp = t_2;
	} else if (y <= -1.1e-135) {
		tmp = x + (x * z);
	} else if (y <= 1.5e-39) {
		tmp = x - (z * t);
	} else if (y <= 1.45e+242) {
		tmp = t_2;
	} else if (y <= 3.5e+301) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (y * t)
    if (y <= (-1d+257)) then
        tmp = t_1
    else if (y <= (-1.4d+45)) then
        tmp = t_2
    else if (y <= (-1.1d-135)) then
        tmp = x + (x * z)
    else if (y <= 1.5d-39) then
        tmp = x - (z * t)
    else if (y <= 1.45d+242) then
        tmp = t_2
    else if (y <= 3.5d+301) then
        tmp = t_1
    else
        tmp = y * t
    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 = x + (y * t);
	double tmp;
	if (y <= -1e+257) {
		tmp = t_1;
	} else if (y <= -1.4e+45) {
		tmp = t_2;
	} else if (y <= -1.1e-135) {
		tmp = x + (x * z);
	} else if (y <= 1.5e-39) {
		tmp = x - (z * t);
	} else if (y <= 1.45e+242) {
		tmp = t_2;
	} else if (y <= 3.5e+301) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (y * t)
	tmp = 0
	if y <= -1e+257:
		tmp = t_1
	elif y <= -1.4e+45:
		tmp = t_2
	elif y <= -1.1e-135:
		tmp = x + (x * z)
	elif y <= 1.5e-39:
		tmp = x - (z * t)
	elif y <= 1.45e+242:
		tmp = t_2
	elif y <= 3.5e+301:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (y <= -1e+257)
		tmp = t_1;
	elseif (y <= -1.4e+45)
		tmp = t_2;
	elseif (y <= -1.1e-135)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 1.5e-39)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 1.45e+242)
		tmp = t_2;
	elseif (y <= 3.5e+301)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (y <= -1e+257)
		tmp = t_1;
	elseif (y <= -1.4e+45)
		tmp = t_2;
	elseif (y <= -1.1e-135)
		tmp = x + (x * z);
	elseif (y <= 1.5e-39)
		tmp = x - (z * t);
	elseif (y <= 1.45e+242)
		tmp = t_2;
	elseif (y <= 3.5e+301)
		tmp = t_1;
	else
		tmp = y * t;
	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[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+257], t$95$1, If[LessEqual[y, -1.4e+45], t$95$2, If[LessEqual[y, -1.1e-135], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-39], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+242], t$95$2, If[LessEqual[y, 3.5e+301], t$95$1, N[(y * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.00000000000000003e257 or 1.44999999999999999e242 < y < 3.4999999999999999e301

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 86.1%

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

      4. fma-define 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in t around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. distribute-lft-neg-out 93.0%

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

      3. *-commutative 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in x around inf 65.7%

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

      1. neg-mul-1 65.7%

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

      2. unsub-neg 65.7%

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

   10. Simplified 65.7%

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

   if -1.00000000000000003e257 < y < -1.4e45 or 1.50000000000000014e-39 < y < 1.44999999999999999e242

   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 65.9%

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

   4. Taylor expanded in y around inf 53.8%

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

      1. *-commutative 53.8%

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

   6. Simplified 53.8%

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

   if -1.4e45 < y < -1.1e-135

   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 79.5%

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

      1. mul-1-neg 79.5%

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

      2. distribute-rgt-neg-in 79.5%

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

      3. sub-neg 79.5%

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

      4. +-commutative 79.5%

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

      5. distribute-neg-in 79.5%

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

      6. unsub-neg 79.5%

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

      7. remove-double-neg 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0 61.9%

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

   if -1.1e-135 < y < 1.50000000000000014e-39

   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 86.6%

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

   4. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

      3. *-commutative 82.6%

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

   6. Simplified 82.6%

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

   if 3.4999999999999999e301 < 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 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 75.2%

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

      1. *-commutative 75.2%

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

   8. Simplified 75.2%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-135}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+242}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -160:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-226}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 90000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* z (- x t))) (t_3 (+ x (* y t))))
   (if (<= z -160.0)
     t_2
     (if (<= z -1e-226)
       t_3
       (if (<= z 4.4e-239)
         t_1
         (if (<= z 1.55e-32) t_3 (if (<= z 90000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -160.0) {
		tmp = t_2;
	} else if (z <= -1e-226) {
		tmp = t_3;
	} else if (z <= 4.4e-239) {
		tmp = t_1;
	} else if (z <= 1.55e-32) {
		tmp = t_3;
	} else if (z <= 90000.0) {
		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 * (1.0d0 - y)
    t_2 = z * (x - t)
    t_3 = x + (y * t)
    if (z <= (-160.0d0)) then
        tmp = t_2
    else if (z <= (-1d-226)) then
        tmp = t_3
    else if (z <= 4.4d-239) then
        tmp = t_1
    else if (z <= 1.55d-32) then
        tmp = t_3
    else if (z <= 90000.0d0) 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 * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -160.0) {
		tmp = t_2;
	} else if (z <= -1e-226) {
		tmp = t_3;
	} else if (z <= 4.4e-239) {
		tmp = t_1;
	} else if (z <= 1.55e-32) {
		tmp = t_3;
	} else if (z <= 90000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = z * (x - t)
	t_3 = x + (y * t)
	tmp = 0
	if z <= -160.0:
		tmp = t_2
	elif z <= -1e-226:
		tmp = t_3
	elif z <= 4.4e-239:
		tmp = t_1
	elif z <= 1.55e-32:
		tmp = t_3
	elif z <= 90000.0:
		tmp = t_1
	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(x - t))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -160.0)
		tmp = t_2;
	elseif (z <= -1e-226)
		tmp = t_3;
	elseif (z <= 4.4e-239)
		tmp = t_1;
	elseif (z <= 1.55e-32)
		tmp = t_3;
	elseif (z <= 90000.0)
		tmp = t_1;
	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 * (x - t);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -160.0)
		tmp = t_2;
	elseif (z <= -1e-226)
		tmp = t_3;
	elseif (z <= 4.4e-239)
		tmp = t_1;
	elseif (z <= 1.55e-32)
		tmp = t_3;
	elseif (z <= 90000.0)
		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[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -160.0], t$95$2, If[LessEqual[z, -1e-226], t$95$3, If[LessEqual[z, 4.4e-239], t$95$1, If[LessEqual[z, 1.55e-32], t$95$3, If[LessEqual[z, 90000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -160 or 9e4 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-rgt-neg-in 84.6%

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

      3. sub-neg 84.6%

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

      4. +-commutative 84.6%

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

      5. distribute-neg-in 84.6%

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

      6. unsub-neg 84.6%

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

      7. remove-double-neg 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in x around -inf 81.3%

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

      1. distribute-lft-out 81.3%

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

      2. mul-1-neg 81.3%

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

      3. *-commutative 81.3%

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

      4. fma-define 82.1%

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

      5. sub-neg 82.1%

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

      6. metadata-eval 82.1%

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

      7. +-commutative 82.1%

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

      8. mul-1-neg 82.1%

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

      9. unsub-neg 82.1%

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

   8. Simplified 82.1%

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

   9. Taylor expanded in z around inf 84.6%

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

       1. neg-mul-1 84.6%

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

       2. sub-neg 84.6%

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

   11. Simplified 84.6%

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

   if -160 < z < -9.99999999999999921e-227 or 4.39999999999999965e-239 < z < 1.55000000000000005e-32

   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 85.6%

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

   4. Taylor expanded in y around inf 76.6%

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

      1. *-commutative 76.6%

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

   6. Simplified 76.6%

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

   if -9.99999999999999921e-227 < z < 4.39999999999999965e-239 or 1.55000000000000005e-32 < z < 9e4

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-define 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 79.3%

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

      1. neg-mul-1 79.3%

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

      2. unsub-neg 79.3%

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

   10. Simplified 79.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -160:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-226}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 90000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-144}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 760000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (- 1.0 y))))
   (if (<= z -0.007)
     t_1
     (if (<= z 2.3e-221)
       t_2
       (if (<= z 3.4e-144) (* y t) (if (<= z 760000.0) 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 <= -0.007) {
		tmp = t_1;
	} else if (z <= 2.3e-221) {
		tmp = t_2;
	} else if (z <= 3.4e-144) {
		tmp = y * t;
	} else if (z <= 760000.0) {
		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 <= (-0.007d0)) then
        tmp = t_1
    else if (z <= 2.3d-221) then
        tmp = t_2
    else if (z <= 3.4d-144) then
        tmp = y * t
    else if (z <= 760000.0d0) 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 <= -0.007) {
		tmp = t_1;
	} else if (z <= 2.3e-221) {
		tmp = t_2;
	} else if (z <= 3.4e-144) {
		tmp = y * t;
	} else if (z <= 760000.0) {
		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 <= -0.007:
		tmp = t_1
	elif z <= 2.3e-221:
		tmp = t_2
	elif z <= 3.4e-144:
		tmp = y * t
	elif z <= 760000.0:
		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 <= -0.007)
		tmp = t_1;
	elseif (z <= 2.3e-221)
		tmp = t_2;
	elseif (z <= 3.4e-144)
		tmp = Float64(y * t);
	elseif (z <= 760000.0)
		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 <= -0.007)
		tmp = t_1;
	elseif (z <= 2.3e-221)
		tmp = t_2;
	elseif (z <= 3.4e-144)
		tmp = y * t;
	elseif (z <= 760000.0)
		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, -0.007], t$95$1, If[LessEqual[z, 2.3e-221], t$95$2, If[LessEqual[z, 3.4e-144], N[(y * t), $MachinePrecision], If[LessEqual[z, 760000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00700000000000000015 or 7.6e5 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-rgt-neg-in 83.3%

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

      3. sub-neg 83.3%

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

      4. +-commutative 83.3%

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

      5. distribute-neg-in 83.3%

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

      6. unsub-neg 83.3%

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

      7. remove-double-neg 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in x around -inf 80.0%

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

      1. distribute-lft-out 80.0%

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

      2. mul-1-neg 80.0%

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

      3. *-commutative 80.0%

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

      4. fma-define 80.8%

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

      5. sub-neg 80.8%

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

      6. metadata-eval 80.8%

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

      7. +-commutative 80.8%

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

      8. mul-1-neg 80.8%

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

      9. unsub-neg 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in t around inf 47.6%

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

   if -0.00700000000000000015 < z < 2.3e-221 or 3.40000000000000017e-144 < z < 7.6e5

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-define 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-lft-neg-out 99.4%

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

      3. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around inf 60.7%

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

      1. neg-mul-1 60.7%

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

      2. unsub-neg 60.7%

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

   10. Simplified 60.7%

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

   if 2.3e-221 < z < 3.40000000000000017e-144

   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 96.7%

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

      1. *-commutative 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

   8. Simplified 67.1%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-144}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 760000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-37} \lor \neg \left(t \leq 3.05 \cdot 10^{-55}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.6e-37) (not (<= t 3.05e-55)))
   (+ x (* t (- y z)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.6e-37) || !(t <= 3.05e-55)) {
		tmp = x + (t * (y - z));
	} 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 ((t <= (-8.6d-37)) .or. (.not. (t <= 3.05d-55))) then
        tmp = x + (t * (y - z))
    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 ((t <= -8.6e-37) || !(t <= 3.05e-55)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.6e-37) or not (t <= 3.05e-55):
		tmp = x + (t * (y - z))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.6e-37) || !(t <= 3.05e-55))
		tmp = Float64(x + Float64(t * Float64(y - z)));
	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 ((t <= -8.6e-37) || ~((t <= 3.05e-55)))
		tmp = x + (t * (y - z));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.6e-37], N[Not[LessEqual[t, 3.05e-55]], $MachinePrecision]], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.59999999999999936e-37 or 3.0500000000000001e-55 < t

   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 85.7%

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

   if -8.59999999999999936e-37 < t < 3.0500000000000001e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. distribute-rgt-neg-in 87.4%

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

      3. sub-neg 87.4%

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

      4. +-commutative 87.4%

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

      5. distribute-neg-in 87.4%

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

      6. unsub-neg 87.4%

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

      7. remove-double-neg 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-37} \lor \neg \left(t \leq 3.05 \cdot 10^{-55}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 28000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7200.0) t_1 (if (<= z 28000.0) (+ x (* y (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7200.0) {
		tmp = t_1;
	} else if (z <= 28000.0) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + 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 = z * (x - t)
    if (z <= (-7200.0d0)) then
        tmp = t_1
    else if (z <= 28000.0d0) then
        tmp = x + (y * (t - x))
    else
        tmp = x + 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 * (x - t);
	double tmp;
	if (z <= -7200.0) {
		tmp = t_1;
	} else if (z <= 28000.0) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7200.0:
		tmp = t_1
	elif z <= 28000.0:
		tmp = x + (y * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7200.0)
		tmp = t_1;
	elseif (z <= 28000.0)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -7200.0)
		tmp = t_1;
	elseif (z <= 28000.0)
		tmp = x + (y * (t - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7200.0], t$95$1, If[LessEqual[z, 28000.0], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7200

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-rgt-neg-in 85.4%

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

      3. sub-neg 85.4%

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

      4. +-commutative 85.4%

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

      5. distribute-neg-in 85.4%

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

      6. unsub-neg 85.4%

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

      7. remove-double-neg 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in x around -inf 80.4%

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

      1. distribute-lft-out 80.4%

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

      2. mul-1-neg 80.4%

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

      3. *-commutative 80.4%

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

      4. fma-define 82.1%

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

      5. sub-neg 82.1%

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

      6. metadata-eval 82.1%

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

      7. +-commutative 82.1%

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

      8. mul-1-neg 82.1%

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

      9. unsub-neg 82.1%

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

   8. Simplified 82.1%

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

   9. Taylor expanded in z around inf 85.4%

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

       1. neg-mul-1 85.4%

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

       2. sub-neg 85.4%

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

   11. Simplified 85.4%

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

   if -7200 < z < 28000

   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 92.5%

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

      1. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   if 28000 < 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 83.9%

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

      1. mul-1-neg 83.9%

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

      2. distribute-rgt-neg-in 83.9%

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

      3. sub-neg 83.9%

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

      4. +-commutative 83.9%

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

      5. distribute-neg-in 83.9%

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

      6. unsub-neg 83.9%

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

      7. remove-double-neg 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7200:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 28000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2900000 \lor \neg \left(z \leq 220000\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2900000.0) (not (<= z 220000.0))) (* z (- t)) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2900000.0) || !(z <= 220000.0)) {
		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 <= (-2900000.0d0)) .or. (.not. (z <= 220000.0d0))) 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 <= -2900000.0) || !(z <= 220000.0)) {
		tmp = z * -t;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2900000.0) or not (z <= 220000.0):
		tmp = z * -t
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2900000.0) || !(z <= 220000.0))
		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 <= -2900000.0) || ~((z <= 220000.0)))
		tmp = z * -t;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2900000.0], N[Not[LessEqual[z, 220000.0]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e6 or 2.2e5 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-rgt-neg-in 84.6%

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

      3. sub-neg 84.6%

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

      4. +-commutative 84.6%

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

      5. distribute-neg-in 84.6%

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

      6. unsub-neg 84.6%

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

      7. remove-double-neg 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in x around -inf 81.3%

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

      1. distribute-lft-out 81.3%

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

      2. mul-1-neg 81.3%

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

      3. *-commutative 81.3%

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

      4. fma-define 82.1%

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

      5. sub-neg 82.1%

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

      6. metadata-eval 82.1%

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

      7. +-commutative 82.1%

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

      8. mul-1-neg 82.1%

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

      9. unsub-neg 82.1%

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

   8. Simplified 82.1%

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

   9. Taylor expanded in t around inf 48.3%

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

   if -2.9e6 < z < 2.2e5

   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 92.5%

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

      1. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in x around 0 40.7%

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

      1. *-commutative 40.7%

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

   8. Simplified 40.7%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2900000 \lor \neg \left(z \leq 220000\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-95} \lor \neg \left(y \leq 1.1 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.75e-95) (not (<= y 1.1e-36))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.75e-95) || !(y <= 1.1e-36)) {
		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 <= (-2.75d-95)) .or. (.not. (y <= 1.1d-36))) 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 <= -2.75e-95) || !(y <= 1.1e-36)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.75e-95) or not (y <= 1.1e-36):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.75e-95) || !(y <= 1.1e-36))
		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 <= -2.75e-95) || ~((y <= 1.1e-36)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.75e-95], N[Not[LessEqual[y, 1.1e-36]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.75000000000000001e-95 or 1.1e-36 < 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 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in x around 0 42.6%

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

      1. *-commutative 42.6%

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

   8. Simplified 42.6%

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

   if -2.75000000000000001e-95 < y < 1.1e-36

   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 84.6%

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

   4. Taylor expanded in x around inf 39.1%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-95} \lor \neg \left(y \leq 1.1 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 18.4% 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 68.0%

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

4. Taylor expanded in x around inf 18.4%

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

5. Final simplification 18.4%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.6% 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 2024044 
(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))))