Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.2% → 98.4%

Time: 7.3s

Alternatives: 9

Speedup: 0.6×

• 25.0% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 93.2% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-46}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ (- y x) t) z x)))
   (if (<= t -9.2e-8) t_1 (if (<= t 1e-46) (+ x (/ (* (- y x) z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(((y - x) / t), z, x);
	double tmp;
	if (t <= -9.2e-8) {
		tmp = t_1;
	} else if (t <= 1e-46) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(Float64(y - x) / t), z, x)
	tmp = 0.0
	if (t <= -9.2e-8)
		tmp = t_1;
	elseif (t <= 1e-46)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[t, -9.2e-8], t$95$1, If[LessEqual[t, 1e-46], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.2000000000000003e-8 or 1.00000000000000002e-46 < t

   1. Initial program 88.9%

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

   3. Applied rewrites 98.4%

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

   if -9.2000000000000003e-8 < t < 1.00000000000000002e-46

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 93.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e+139) (fma (/ z t) y x) (fma (/ (- y x) t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e+139) {
		tmp = fma((z / t), y, x);
	} else {
		tmp = fma(((y - x) / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e+139)
		tmp = fma(Float64(z / t), y, x);
	else
		tmp = fma(Float64(Float64(y - x) / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e+139], N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0500000000000001e139

   1. Initial program 90.1%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 85.9%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. +-commutative N/A

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

      8. remove-double-neg N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-/.f64 92.2

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

   6. Applied rewrites 92.2%

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

   if -2.0500000000000001e139 < y

   1. Initial program 93.7%

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

   3. Applied rewrites 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ z t) y x)))
   (if (<= y -3.2e-52) t_1 (if (<= y 4.8e-22) (* (- 1.0 (/ z t)) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((z / t), y, x);
	double tmp;
	if (y <= -3.2e-52) {
		tmp = t_1;
	} else if (y <= 4.8e-22) {
		tmp = (1.0 - (z / t)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(z / t), y, x)
	tmp = 0.0
	if (y <= -3.2e-52)
		tmp = t_1;
	elseif (y <= 4.8e-22)
		tmp = Float64(Float64(1.0 - Float64(z / t)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[y, -3.2e-52], t$95$1, If[LessEqual[y, 4.8e-22], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e-52 or 4.80000000000000005e-22 < y

   1. Initial program 91.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 83.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. +-commutative N/A

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

      8. remove-double-neg N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-/.f64 87.7

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

   6. Applied rewrites 87.7%

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

   if -3.2000000000000001e-52 < y < 4.80000000000000005e-22

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. mul-1-neg N/A

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

      11. associate-/l* N/A

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

      12. distribute-lft-neg-in N/A

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

      13. distribute-lft-out-- N/A

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

      14. distribute-lft-neg-out N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. distribute-lft-neg-out N/A

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

      18. distribute-lft-out-- N/A

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

   4. Applied rewrites 84.3%

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

Alternative 4: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (/ (* (- y x) z) t)) (- INFINITY))
   (* (/ (- z) t) x)
   (fma (/ z t) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + (((y - x) * z) / t)) <= -((double) INFINITY)) {
		tmp = (-z / t) * x;
	} else {
		tmp = fma((z / t), y, x);
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0

   1. Initial program 81.6%

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

   2. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. mul-1-neg N/A

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

      11. associate-/l* N/A

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

      12. distribute-lft-neg-in N/A

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

      13. distribute-lft-out-- N/A

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

      14. distribute-lft-neg-out N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. distribute-lft-neg-out N/A

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

      18. distribute-lft-out-- N/A

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(z\right)}{t} \cdot x \]

      4. lower-neg.f64 54.0

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

   7. Applied rewrites 54.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 95.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 77.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. +-commutative N/A

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

      8. remove-double-neg N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-/.f64 78.9

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

   6. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\ \;\;\;\;\frac{-z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (/ (* (- y x) z) t)) (- INFINITY))
   (* (/ (- z) t) x)
   (fma (/ y t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + (((y - x) * z) / t)) <= -((double) INFINITY)) {
		tmp = (-z / t) * x;
	} else {
		tmp = fma((y / t), z, x);
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0

   1. Initial program 81.6%

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

   2. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. mul-1-neg N/A

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

      11. associate-/l* N/A

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

      12. distribute-lft-neg-in N/A

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

      13. distribute-lft-out-- N/A

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

      14. distribute-lft-neg-out N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. distribute-lft-neg-out N/A

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

      18. distribute-lft-out-- N/A

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(z\right)}{t} \cdot x \]

      4. lower-neg.f64 54.0

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

   7. Applied rewrites 54.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 95.4%

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

   3. Applied rewrites 91.5%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 75.5

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

   6. Applied rewrites 75.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{t}}, z, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e+60) x (if (<= t 4.1e+116) (* (/ z t) y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e+60) {
		tmp = x;
	} else if (t <= 4.1e+116) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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+60)) then
        tmp = x
    else if (t <= 4.1d+116) then
        tmp = (z / t) * y
    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+60) {
		tmp = x;
	} else if (t <= 4.1e+116) {
		tmp = (z / t) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e+60:
		tmp = x
	elif t <= 4.1e+116:
		tmp = (z / t) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e+60)
		tmp = x;
	elseif (t <= 4.1e+116)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e+60)
		tmp = x;
	elseif (t <= 4.1e+116)
		tmp = (z / t) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e+60], x, If[LessEqual[t, 4.1e+116], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999931e60 or 4.0999999999999998e116 < t

   1. Initial program 84.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

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

   if -6.49999999999999931e60 < t < 4.0999999999999998e116

   1. Initial program 97.8%

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

   3. Applied rewrites 90.2%

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

   4. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 48.6

         \[\leadsto \frac{z}{t} \cdot y \]

   6. Applied rewrites 48.6%

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

Alternative 7: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e+61) x (if (<= t 2.8e+111) (/ (* z y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e+61) {
		tmp = x;
	} else if (t <= 2.8e+111) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-3.7d+61)) then
        tmp = x
    else if (t <= 2.8d+111) then
        tmp = (z * 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 (t <= -3.7e+61) {
		tmp = x;
	} else if (t <= 2.8e+111) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.7e+61:
		tmp = x
	elif t <= 2.8e+111:
		tmp = (z * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.7e+61)
		tmp = x;
	elseif (t <= 2.8e+111)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.7e+61)
		tmp = x;
	elseif (t <= 2.8e+111)
		tmp = (z * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.7e+61], x, If[LessEqual[t, 2.8e+111], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -3.70000000000000003e61 or 2.7999999999999999e111 < t

   1. Initial program 84.6%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

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

   if -3.70000000000000003e61 < t < 2.7999999999999999e111

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. remove-double-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot z\right)\right)\right)}{t} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(-1 \cdot \left(y \cdot z\right)\right)}{t} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(-1 \cdot \left(z \cdot y\right)\right)}{t} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(-1 \cdot z\right) \cdot y\right)}{t} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(-1 \cdot z\right)\right) \cdot y}{t} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(-1 \cdot z\right)\right) \cdot y}{t} \]

      8. distribute-lft-neg-out N/A

         \[\leadsto \frac{\left(\left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) \cdot y}{t} \]

      9. metadata-eval N/A

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

      10. *-lft-identity 46.9

          \[\leadsto \frac{z \cdot y}{t} \]

   4. Applied rewrites 46.9%

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

Alternative 8: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.1e+86) x (if (<= x 1.75e-25) (* (/ y t) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.1e+86) {
		tmp = x;
	} else if (x <= 1.75e-25) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-4.1d+86)) then
        tmp = x
    else if (x <= 1.75d-25) then
        tmp = (y / t) * z
    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 <= -4.1e+86) {
		tmp = x;
	} else if (x <= 1.75e-25) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.1e+86:
		tmp = x
	elif x <= 1.75e-25:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.1e+86)
		tmp = x;
	elseif (x <= 1.75e-25)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.1e+86)
		tmp = x;
	elseif (x <= 1.75e-25)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.1e+86], x, If[LessEqual[x, 1.75e-25], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0999999999999999e86 or 1.7500000000000001e-25 < x

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.8%

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

   if -4.0999999999999999e86 < x < 1.7500000000000001e-25

   1. Initial program 94.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. remove-double-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(y \cdot z\right)\right)\right)}{t} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(-1 \cdot \left(y \cdot z\right)\right)}{t} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(-1 \cdot \left(z \cdot y\right)\right)}{t} \]

      5. associate-*l* N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(-1 \cdot z\right) \cdot y\right)}{t} \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(-1 \cdot z\right)\right) \cdot y}{t} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(-1 \cdot z\right)\right) \cdot y}{t} \]

      8. distribute-lft-neg-out N/A

         \[\leadsto \frac{\left(\left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) \cdot y}{t} \]

      9. metadata-eval N/A

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

      10. *-lft-identity 53.4

          \[\leadsto \frac{z \cdot y}{t} \]

   4. Applied rewrites 53.4%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y}{t} \]

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 52.7

         \[\leadsto \frac{y}{t} \cdot z \]

   6. Applied rewrites 52.7%

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

Alternative 9: 38.7% accurate, 12.7× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 93.2%

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

2. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 38.7%

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

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y x) z) t)))