Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.1% → 97.5%

Time: 9.1s

Alternatives: 12

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. +-commutative 94.3%

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

   2. associate-/l* 97.4%

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

   3. fma-define 97.4%

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

3. Simplified 97.4%

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

Alternative 2: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e+52)
   (* x (/ (- t z) t))
   (if (<= x 3.5e-24) (+ x (/ y (/ t z))) (- x (/ x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e+52) {
		tmp = x * ((t - z) / t);
	} else if (x <= 3.5e-24) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x / (t / z));
	}
	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 <= (-1.4d+52)) then
        tmp = x * ((t - z) / t)
    else if (x <= 3.5d-24) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (x / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e+52) {
		tmp = x * ((t - z) / t);
	} else if (x <= 3.5e-24) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e+52:
		tmp = x * ((t - z) / t)
	elif x <= 3.5e-24:
		tmp = x + (y / (t / z))
	else:
		tmp = x - (x / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e+52)
		tmp = Float64(x * Float64(Float64(t - z) / t));
	elseif (x <= 3.5e-24)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(x / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.4e+52)
		tmp = x * ((t - z) / t);
	elseif (x <= 3.5e-24)
		tmp = x + (y / (t / z));
	else
		tmp = x - (x / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e+52], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-24], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e52

   1. Initial program 95.2%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in t around 0 97.5%

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

   if -1.4e52 < x < 3.4999999999999996e-24

   1. Initial program 95.2%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around inf 85.4%

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

      1. associate-*r/ 87.7%

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

   7. Simplified 87.7%

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

      1. clear-num 87.5%

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

      2. div-inv 87.7%

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

   9. Applied egg-rr 87.7%

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

   if 3.4999999999999996e-24 < x

   1. Initial program 92.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 86.5%

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

      1. neg-mul-1 86.5%

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

   9. Simplified 86.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e+52)
   (* x (/ (- t z) t))
   (if (<= x 3.5e-24) (+ x (/ y (/ t z))) (* x (- 1.0 (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e+52) {
		tmp = x * ((t - z) / t);
	} else if (x <= 3.5e-24) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (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 <= (-6d+52)) then
        tmp = x * ((t - z) / t)
    else if (x <= 3.5d-24) then
        tmp = x + (y / (t / z))
    else
        tmp = x * (1.0d0 - (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 <= -6e+52) {
		tmp = x * ((t - z) / t);
	} else if (x <= 3.5e-24) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e+52:
		tmp = x * ((t - z) / t)
	elif x <= 3.5e-24:
		tmp = x + (y / (t / z))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e+52)
		tmp = Float64(x * Float64(Float64(t - z) / t));
	elseif (x <= 3.5e-24)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6e+52)
		tmp = x * ((t - z) / t);
	elseif (x <= 3.5e-24)
		tmp = x + (y / (t / z));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e+52], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-24], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6e52

   1. Initial program 95.2%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in t around 0 97.5%

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

   if -6e52 < x < 3.4999999999999996e-24

   1. Initial program 95.2%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around inf 85.4%

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

      1. associate-*r/ 87.7%

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

   7. Simplified 87.7%

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

      1. clear-num 87.5%

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

      2. div-inv 87.7%

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

   9. Applied egg-rr 87.7%

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

   if 3.4999999999999996e-24 < x

   1. Initial program 92.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   7. Simplified 86.5%

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

Alternative 4: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e+52)
   (* x (/ (- t z) t))
   (if (<= x 4.4e-24) (+ x (* y (/ z t))) (* x (- 1.0 (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e+52) {
		tmp = x * ((t - z) / t);
	} else if (x <= 4.4e-24) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.6d+52)) then
        tmp = x * ((t - z) / t)
    else if (x <= 4.4d-24) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e+52) {
		tmp = x * ((t - z) / t);
	} else if (x <= 4.4e-24) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e+52:
		tmp = x * ((t - z) / t)
	elif x <= 4.4e-24:
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e+52)
		tmp = Float64(x * Float64(Float64(t - z) / t));
	elseif (x <= 4.4e-24)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e+52)
		tmp = x * ((t - z) / t);
	elseif (x <= 4.4e-24)
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e+52], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-24], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6e52

   1. Initial program 95.2%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in t around 0 97.5%

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

   if -2.6e52 < x < 4.40000000000000003e-24

   1. Initial program 95.2%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around inf 85.4%

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

      1. associate-*r/ 87.7%

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

   7. Simplified 87.7%

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

   if 4.40000000000000003e-24 < x

   1. Initial program 92.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   7. Simplified 86.5%

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

Alternative 5: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+35} \lor \neg \left(z \leq 6.4 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+35) (not (<= z 6.4e+22))) (* z (/ x (- t))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+35) || !(z <= 6.4e+22)) {
		tmp = z * (x / -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 ((z <= (-2.2d+35)) .or. (.not. (z <= 6.4d+22))) then
        tmp = z * (x / -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 ((z <= -2.2e+35) || !(z <= 6.4e+22)) {
		tmp = z * (x / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+35) or not (z <= 6.4e+22):
		tmp = z * (x / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+35) || !(z <= 6.4e+22))
		tmp = Float64(z * Float64(x / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e+35) || ~((z <= 6.4e+22)))
		tmp = z * (x / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+35], N[Not[LessEqual[z, 6.4e+22]], $MachinePrecision]], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e35 or 6.4e22 < z

   1. Initial program 87.7%

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

   3. Taylor expanded in y around 0 52.8%

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

      1. neg-mul-1 59.0%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in t around 0 50.2%

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

      1. neg-mul-1 50.2%

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

      2. +-commutative 50.2%

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

      3. *-commutative 50.2%

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

      4. distribute-rgt-neg-in 50.2%

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

      5. distribute-lft-out 52.0%

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

   8. Simplified 52.0%

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

   9. Taylor expanded in t around 0 45.5%

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

       1. associate-*r* 45.5%

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

       2. mul-1-neg 45.5%

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

   11. Simplified 45.5%

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

       1. associate-/l* 48.1%

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

       2. distribute-lft-neg-out 48.1%

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

       3. clear-num 48.1%

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

       4. div-inv 48.1%

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

       5. div-inv 48.1%

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

       6. clear-num 48.1%

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

       7. add-sqr-sqrt 26.6%

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

       8. sqrt-unprod 27.5%

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

       9. sqr-neg 27.5%

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

       10. sqrt-unprod 3.4%

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

       11. add-sqr-sqrt 7.1%

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

       12. associate-/l* 6.2%

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

       13. *-commutative 6.2%

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

       14. associate-/l* 6.3%

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

       15. add-sqr-sqrt 2.5%

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

       16. sqrt-unprod 26.7%

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

       17. sqr-neg 26.7%

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

       18. sqrt-unprod 25.7%

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

       19. add-sqr-sqrt 47.3%

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

   13. Applied egg-rr 47.3%

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

   if -2.1999999999999999e35 < z < 6.4e22

   1. Initial program 99.9%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 53.7%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+35} \lor \neg \left(z \leq 6.4 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e-23) x (if (<= t 6.8) (* x (/ (- z) t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-23) {
		tmp = x;
	} else if (t <= 6.8) {
		tmp = x * (-z / 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 (t <= (-6.5d-23)) then
        tmp = x
    else if (t <= 6.8d0) then
        tmp = x * (-z / 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 (t <= -6.5e-23) {
		tmp = x;
	} else if (t <= 6.8) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e-23:
		tmp = x
	elif t <= 6.8:
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e-23)
		tmp = x;
	elseif (t <= 6.8)
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e-23)
		tmp = x;
	elseif (t <= 6.8)
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e-23], x, If[LessEqual[t, 6.8], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5e-23 or 6.79999999999999982 < t

   1. Initial program 89.7%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 55.1%

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

   if -6.5e-23 < t < 6.79999999999999982

   1. Initial program 99.8%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

   7. Simplified 56.1%

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

   8. Taylor expanded in z around inf 47.5%

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

      1. associate-*r/ 47.5%

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

      2. mul-1-neg 47.5%

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

   10. Simplified 47.5%

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

Alternative 7: 39.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -7.5e+168) (* t (/ x t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.5e+168) {
		tmp = t * (x / 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 (x <= (-7.5d+168)) then
        tmp = t * (x / 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 (x <= -7.5e+168) {
		tmp = t * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.5e+168:
		tmp = t * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.5e+168)
		tmp = Float64(t * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.5e+168)
		tmp = t * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.5e+168], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -7.4999999999999999e168

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 91.2%

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

      1. neg-mul-1 95.5%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in t around 0 65.2%

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

      1. neg-mul-1 65.2%

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

      2. +-commutative 65.2%

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

      3. *-commutative 65.2%

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

      4. distribute-rgt-neg-in 65.2%

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

      5. distribute-lft-out 74.3%

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

   8. Simplified 74.3%

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

   9. Taylor expanded in t around inf 19.9%

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

       1. *-commutative 19.9%

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

   11. Simplified 19.9%

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

       1. *-commutative 19.9%

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

       2. associate-/l* 56.4%

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

   13. Applied egg-rr 56.4%

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

   if -7.4999999999999999e168 < x

   1. Initial program 94.2%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 34.4%

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

Alternative 8: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. associate-/l* 97.4%

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

3. Simplified 97.4%

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

   1. clear-num 97.2%

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

   2. un-div-inv 97.4%

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

6. Applied egg-rr 97.4%

   \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
7. Add Preprocessing

Alternative 9: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. associate-/l* 97.4%

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

3. Simplified 97.4%

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

Alternative 10: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. associate-/l* 97.4%

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

3. Simplified 97.4%

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

5. Taylor expanded in y around 0 90.4%

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

   1. +-commutative 90.4%

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

   2. associate-*r/ 88.9%

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

   3. mul-1-neg 88.9%

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

   4. associate-/l* 91.8%

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

   5. distribute-lft-neg-out 91.8%

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

   6. distribute-rgt-out 97.4%

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

   7. sub-neg 97.4%

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

   8. associate-*l/ 94.3%

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

   9. associate-*r/ 94.3%

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

7. Simplified 94.3%

   \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{t}} \]
8. Add Preprocessing

Alternative 11: 65.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (1.0d0 - (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. associate-/l* 97.4%

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

3. Simplified 97.4%

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

5. Taylor expanded in x around inf 63.4%

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

   1. mul-1-neg 63.4%

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

   2. unsub-neg 63.4%

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

7. Simplified 63.4%

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

Alternative 12: 39.3% 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 94.3%

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

   1. associate-/l* 97.4%

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

3. Simplified 97.4%

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

5. Taylor expanded in z around 0 34.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	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 < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1805102239106601/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (* (/ z t) (- x y))) (if (< x 855006432740143/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z))))))

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