Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.4% → 99.8%

Time: 1.9min

Alternatives: 10

Speedup: 1.0×

Specification

Math

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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, a)
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), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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, a)
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), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - t}\right), y, 60, x, 60\right) + a \cdot 120 \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ (134-z0z1z2z3z4 (/ -1 (- z t)) y 60 x 60) (* a 120)))

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

   2. frac-2neg N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} + a \cdot 120 \]

   3. mult-flip N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)}} + a \cdot 120 \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{\frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right)} + a \cdot 120 \]

   5. *-rgt-identity N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) \cdot 1\right)} + a \cdot 120 \]

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

      \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \left(x - y\right)\right) \cdot 1\right)\right)} + a \cdot 120 \]

   7. *-rgt-identity N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)\right) + a \cdot 120 \]

   8. lift-*.f64 N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)\right) + a \cdot 120 \]

   9. lift--.f64 N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \color{blue}{\left(x - y\right)}\right)\right) + a \cdot 120 \]

   10. distribute-rgt-out-- N/A

       \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(x \cdot 60 - y \cdot 60\right)}\right)\right) + a \cdot 120 \]

   11. sub-negate N/A

       \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(y \cdot 60 - x \cdot 60\right)} + a \cdot 120 \]

   12. lower-134-z0z1z2z3z4 N/A

       \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), y, 60, x, 60\right)} + a \cdot 120 \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), y, 60, x, 60\right) + a \cdot 120 \]

   14. frac-2neg-rev N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - t}\right)}, y, 60, x, 60\right) + a \cdot 120 \]

   15. lower-/.f64 99.8%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - t}\right)}, y, 60, x, 60\right) + a \cdot 120 \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - t}\right), y, 60, x, 60\right)} + a \cdot 120 \]
4. Add Preprocessing

Alternative 2: 89.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{if}\;y \leq -920000000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{6643344963566725}{7067388259113537318333190002971674063309935587502475832486424805170479104}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ (* -60 (/ y (- z t))) (* a 120))))
  (if (<= y -920000000000000000)
    t_1
    (if (<=
         y
         6643344963566725/7067388259113537318333190002971674063309935587502475832486424805170479104)
      (+ (* 60 (/ x (- z t))) (* a 120))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * (y / (z - t))) + (a * 120.0);
	double tmp;
	if (y <= -9.2e+17) {
		tmp = t_1;
	} else if (y <= 9.4e-58) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-60.0d0) * (y / (z - t))) + (a * 120.0d0)
    if (y <= (-9.2d+17)) then
        tmp = t_1
    else if (y <= 9.4d-58) then
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * (y / (z - t))) + (a * 120.0);
	double tmp;
	if (y <= -9.2e+17) {
		tmp = t_1;
	} else if (y <= 9.4e-58) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 * (y / (z - t))) + (a * 120.0)
	tmp = 0
	if y <= -9.2e+17:
		tmp = t_1
	elif y <= 9.4e-58:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(a * 120.0))
	tmp = 0.0
	if (y <= -9.2e+17)
		tmp = t_1;
	elseif (y <= 9.4e-58)
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 * (y / (z - t))) + (a * 120.0);
	tmp = 0.0;
	if (y <= -9.2e+17)
		tmp = t_1;
	elseif (y <= 9.4e-58)
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -920000000000000000], t$95$1, If[LessEqual[y, 6643344963566725/7067388259113537318333190002971674063309935587502475832486424805170479104], N[(N[(60 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.2e17 or 9.3999999999999999e-58 < y

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} + a \cdot 120 \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} + a \cdot 120 \]

      3. lower--.f64 76.0%

         \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} + a \cdot 120 \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]

   if -9.2e17 < y < 9.3999999999999999e-58

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} + a \cdot 120 \]

      3. mult-flip N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)}} + a \cdot 120 \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right)} + a \cdot 120 \]

      5. *-rgt-identity N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) \cdot 1\right)} + a \cdot 120 \]

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

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \left(x - y\right)\right) \cdot 1\right)\right)} + a \cdot 120 \]

      7. *-rgt-identity N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)\right) + a \cdot 120 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)\right) + a \cdot 120 \]

      9. lift--.f64 N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \color{blue}{\left(x - y\right)}\right)\right) + a \cdot 120 \]

      10. distribute-rgt-out-- N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(x \cdot 60 - y \cdot 60\right)}\right)\right) + a \cdot 120 \]

      11. sub-negate N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(y \cdot 60 - x \cdot 60\right)} + a \cdot 120 \]

      12. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), y, 60, x, 60\right)} + a \cdot 120 \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), y, 60, x, 60\right) + a \cdot 120 \]

      14. frac-2neg-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - t}\right)}, y, 60, x, 60\right) + a \cdot 120 \]

      15. lower-/.f64 99.8%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - t}\right)}, y, 60, x, 60\right) + a \cdot 120 \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - t}\right), y, 60, x, 60\right)} + a \cdot 120 \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} + a \cdot 120 \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} + a \cdot 120 \]

      3. lower--.f64 75.1%

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} + a \cdot 120 \]

   6. Applied rewrites 75.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 81.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -3099999999999999896533334876964249800205167308886334283362040000083741526987387902368537446004427030739951226815029036893217415655816957778969254797349185177254199416913729178243794021108446847282946886087200767078534297987530948083712:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -25499999999999999528024993055952010542249007939197233513958453954737868247668078447050309476321791611551296703204050146631997321389936393151246862110425088:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \mathbf{elif}\;y \leq 510000000000000022032816663106096486183925973148785287396432843573633510044500020291792739008901828466414977024:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \left(\frac{1}{z - t} \cdot \left(y - x\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     y
     -3099999999999999896533334876964249800205167308886334283362040000083741526987387902368537446004427030739951226815029036893217415655816957778969254797349185177254199416913729178243794021108446847282946886087200767078534297987530948083712)
  (* -60 (/ y (- z t)))
  (if (<=
       y
       -25499999999999999528024993055952010542249007939197233513958453954737868247668078447050309476321791611551296703204050146631997321389936393151246862110425088)
    (+ (* -60 (/ y z)) (* a 120))
    (if (<=
         y
         510000000000000022032816663106096486183925973148785287396432843573633510044500020291792739008901828466414977024)
      (+ (* 60 (/ x (- z t))) (* a 120))
      (* -60 (* (/ 1 (- z t)) (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.1e+234) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2.55e+154) {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	} else if (y <= 5.1e+110) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = -60.0 * ((1.0 / (z - t)) * (y - 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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.1d+234)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-2.55d+154)) then
        tmp = ((-60.0d0) * (y / z)) + (a * 120.0d0)
    else if (y <= 5.1d+110) then
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    else
        tmp = (-60.0d0) * ((1.0d0 / (z - t)) * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.1e+234) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2.55e+154) {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	} else if (y <= 5.1e+110) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = -60.0 * ((1.0 / (z - t)) * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.1e+234:
		tmp = -60.0 * (y / (z - t))
	elif y <= -2.55e+154:
		tmp = (-60.0 * (y / z)) + (a * 120.0)
	elif y <= 5.1e+110:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	else:
		tmp = -60.0 * ((1.0 / (z - t)) * (y - x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.1e+234)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -2.55e+154)
		tmp = Float64(Float64(-60.0 * Float64(y / z)) + Float64(a * 120.0));
	elseif (y <= 5.1e+110)
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(-60.0 * Float64(Float64(1.0 / Float64(z - t)) * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.1e+234)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -2.55e+154)
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	elseif (y <= 5.1e+110)
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	else
		tmp = -60.0 * ((1.0 / (z - t)) * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3099999999999999896533334876964249800205167308886334283362040000083741526987387902368537446004427030739951226815029036893217415655816957778969254797349185177254199416913729178243794021108446847282946886087200767078534297987530948083712], N[(-60 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -25499999999999999528024993055952010542249007939197233513958453954737868247668078447050309476321791611551296703204050146631997321389936393151246862110425088], N[(N[(-60 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 510000000000000022032816663106096486183925973148785287396432843573633510044500020291792739008901828466414977024], N[(N[(60 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120), $MachinePrecision]), $MachinePrecision], N[(-60 * N[(N[(1 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.0999999999999999e234

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

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

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      6. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

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

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\color{blue}{\left(y - x\right)} \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      12. associate-/l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{60}{z - t}\right)\right)} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      16. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      17. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      18. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{-60}}{z - t} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      19. lower--.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \color{blue}{\left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      20. *-commutative N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{120 \cdot \left(\mathsf{neg}\left(a\right)\right)} \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120 \cdot a\right)\right)} \]

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

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      23. lower-*.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      24. metadata-eval 99.8%

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{-120} \cdot a \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{-60}{z - t} \cdot \left(y - x\right) - -120 \cdot a} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y - x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto -60 \cdot \frac{y - x}{z - \color{blue}{t}} \]

   6. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]

   7. Taylor expanded in x around 0

      \[\leadsto -60 \cdot \frac{y}{\color{blue}{z} - t} \]
   8. Step-by-step derivation

   9. Applied rewrites 27.0%

      \[\leadsto -60 \cdot \frac{y}{\color{blue}{z} - t} \]

   if -3.0999999999999999e234 < y < -2.55e154

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} + a \cdot 120 \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} + a \cdot 120 \]

      3. lower--.f64 76.0%

         \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} + a \cdot 120 \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]

   5. Taylor expanded in z around inf

      \[\leadsto -60 \cdot \frac{y}{\color{blue}{z}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. lower-/.f64 55.4%

         \[\leadsto -60 \cdot \frac{y}{z} + a \cdot 120 \]

   7. Applied rewrites 55.4%

      \[\leadsto -60 \cdot \frac{y}{\color{blue}{z}} + a \cdot 120 \]

   if -2.55e154 < y < 5.1000000000000002e110

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} + a \cdot 120 \]

      3. mult-flip N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)}} + a \cdot 120 \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right)} + a \cdot 120 \]

      5. *-rgt-identity N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) \cdot 1\right)} + a \cdot 120 \]

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

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \left(x - y\right)\right) \cdot 1\right)\right)} + a \cdot 120 \]

      7. *-rgt-identity N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)\right) + a \cdot 120 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)\right) + a \cdot 120 \]

      9. lift--.f64 N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \color{blue}{\left(x - y\right)}\right)\right) + a \cdot 120 \]

      10. distribute-rgt-out-- N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\mathsf{neg}\left(\color{blue}{\left(x \cdot 60 - y \cdot 60\right)}\right)\right) + a \cdot 120 \]

      11. sub-negate N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(y \cdot 60 - x \cdot 60\right)} + a \cdot 120 \]

      12. lower-134-z0z1z2z3z4 N/A

          \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), y, 60, x, 60\right)} + a \cdot 120 \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), y, 60, x, 60\right) + a \cdot 120 \]

      14. frac-2neg-rev N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - t}\right)}, y, 60, x, 60\right) + a \cdot 120 \]

      15. lower-/.f64 99.8%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - t}\right)}, y, 60, x, 60\right) + a \cdot 120 \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - t}\right), y, 60, x, 60\right)} + a \cdot 120 \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} + a \cdot 120 \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} + a \cdot 120 \]

      3. lower--.f64 75.1%

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} + a \cdot 120 \]

   6. Applied rewrites 75.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]

   if 5.1000000000000002e110 < y

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

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

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      6. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

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

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\color{blue}{\left(y - x\right)} \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      12. associate-/l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{60}{z - t}\right)\right)} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      16. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      17. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      18. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{-60}}{z - t} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      19. lower--.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \color{blue}{\left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      20. *-commutative N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{120 \cdot \left(\mathsf{neg}\left(a\right)\right)} \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120 \cdot a\right)\right)} \]

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

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      23. lower-*.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      24. metadata-eval 99.8%

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{-120} \cdot a \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{-60}{z - t} \cdot \left(y - x\right) - -120 \cdot a} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y - x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto -60 \cdot \frac{y - x}{z - \color{blue}{t}} \]

   6. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      2. mult-flip N/A

         \[\leadsto -60 \cdot \left(\left(y - x\right) \cdot \color{blue}{\frac{1}{z - t}}\right) \]

      3. lift-/.f64 N/A

         \[\leadsto -60 \cdot \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{z - t}}\right) \]

      4. *-commutative N/A

         \[\leadsto -60 \cdot \left(\frac{1}{z - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

      5. lower-*.f64 50.1%

         \[\leadsto -60 \cdot \left(\frac{1}{z - t} \cdot \color{blue}{\left(y - x\right)}\right) \]

   8. Applied rewrites 50.1%

      \[\leadsto -60 \cdot \left(\frac{1}{z - t} \cdot \color{blue}{\left(y - x\right)}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -4000000000000000053150220288:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 39999999999999998543585179860992:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* 60 (/ (- x y) (- z t))))
       (t_2 (/ (* 60 (- x y)) (- z t))))
  (if (<= t_2 -4000000000000000053150220288)
    t_1
    (if (<= t_2 39999999999999998543585179860992) (* 120 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -4e+27) {
		tmp = t_1;
	} else if (t_2 <= 4e+31) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-4d+27)) then
        tmp = t_1
    else if (t_2 <= 4d+31) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -4e+27) {
		tmp = t_1;
	} else if (t_2 <= 4e+31) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -4e+27:
		tmp = t_1
	elif t_2 <= 4e+31:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -4e+27)
		tmp = t_1;
	elseif (t_2 <= 4e+31)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -4e+27)
		tmp = t_1;
	elseif (t_2 <= 4e+31)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4000000000000000053150220288], t$95$1, If[LessEqual[t$95$2, 39999999999999998543585179860992], N[(120 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.0000000000000001e27 or 3.9999999999999999e31 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if -4.0000000000000001e27 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 3.9999999999999999e31

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.2%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -9999999999999999483531874467312143214394768377282087351960514613084929070487027419252537449089020883885200422613425626021888:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq 1999999999999999996434887128370482831977857737518825000873086679459880803811809298994231532284537120019554351933503330752464420864:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* 60 (- x y)) (- z t))))
  (if (<=
       t_1
       -9999999999999999483531874467312143214394768377282087351960514613084929070487027419252537449089020883885200422613425626021888)
    (* -60 (/ y (- z t)))
    (if (<=
         t_1
         1999999999999999996434887128370482831977857737518825000873086679459880803811809298994231532284537120019554351933503330752464420864)
      (* 120 a)
      (* -60 (/ (- y x) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+124) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 2e+129) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * ((y - x) / z);
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+124)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= 2d+129) then
        tmp = 120.0d0 * a
    else
        tmp = (-60.0d0) * ((y - x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+124) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 2e+129) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * ((y - x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+124:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= 2e+129:
		tmp = 120.0 * a
	else:
		tmp = -60.0 * ((y - x) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+124)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= 2e+129)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(-60.0 * Float64(Float64(y - x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+124)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= 2e+129)
		tmp = 120.0 * a;
	else
		tmp = -60.0 * ((y - x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -9999999999999999483531874467312143214394768377282087351960514613084929070487027419252537449089020883885200422613425626021888], N[(-60 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1999999999999999996434887128370482831977857737518825000873086679459880803811809298994231532284537120019554351933503330752464420864], N[(120 * a), $MachinePrecision], N[(-60 * N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999995e123

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

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

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      6. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

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

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\color{blue}{\left(y - x\right)} \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      12. associate-/l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{60}{z - t}\right)\right)} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      16. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      17. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      18. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{-60}}{z - t} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      19. lower--.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \color{blue}{\left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      20. *-commutative N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{120 \cdot \left(\mathsf{neg}\left(a\right)\right)} \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120 \cdot a\right)\right)} \]

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

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      23. lower-*.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      24. metadata-eval 99.8%

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{-120} \cdot a \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{-60}{z - t} \cdot \left(y - x\right) - -120 \cdot a} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y - x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto -60 \cdot \frac{y - x}{z - \color{blue}{t}} \]

   6. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]

   7. Taylor expanded in x around 0

      \[\leadsto -60 \cdot \frac{y}{\color{blue}{z} - t} \]
   8. Step-by-step derivation

   9. Applied rewrites 27.0%

      \[\leadsto -60 \cdot \frac{y}{\color{blue}{z} - t} \]

   if -9.9999999999999995e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e129

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.2%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 2e129 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

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

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      6. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

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

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\color{blue}{\left(y - x\right)} \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      12. associate-/l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{60}{z - t}\right)\right)} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      16. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      17. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      18. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{-60}}{z - t} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      19. lower--.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \color{blue}{\left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      20. *-commutative N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{120 \cdot \left(\mathsf{neg}\left(a\right)\right)} \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120 \cdot a\right)\right)} \]

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

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      23. lower-*.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      24. metadata-eval 99.8%

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{-120} \cdot a \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{-60}{z - t} \cdot \left(y - x\right) - -120 \cdot a} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y - x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto -60 \cdot \frac{y - x}{z - \color{blue}{t}} \]

   6. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]

   7. Taylor expanded in z around inf

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

      2. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

   9. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := -60 \cdot \frac{y - x}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -9999999999999999483531874467312143214394768377282087351960514613084929070487027419252537449089020883885200422613425626021888:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1999999999999999996434887128370482831977857737518825000873086679459880803811809298994231532284537120019554351933503330752464420864:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* -60 (/ (- y x) z))) (t_2 (/ (* 60 (- x y)) (- z t))))
  (if (<=
       t_2
       -9999999999999999483531874467312143214394768377282087351960514613084929070487027419252537449089020883885200422613425626021888)
    t_1
    (if (<=
         t_2
         1999999999999999996434887128370482831977857737518825000873086679459880803811809298994231532284537120019554351933503330752464420864)
      (* 120 a)
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((y - x) / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+124) {
		tmp = t_1;
	} else if (t_2 <= 2e+129) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * ((y - x) / z)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+124)) then
        tmp = t_1
    else if (t_2 <= 2d+129) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((y - x) / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+124) {
		tmp = t_1;
	} else if (t_2 <= 2e+129) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((y - x) / z)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+124:
		tmp = t_1
	elif t_2 <= 2e+129:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(y - x) / z))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+124)
		tmp = t_1;
	elseif (t_2 <= 2e+129)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * ((y - x) / z);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+124)
		tmp = t_1;
	elseif (t_2 <= 2e+129)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60 * N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -9999999999999999483531874467312143214394768377282087351960514613084929070487027419252537449089020883885200422613425626021888], t$95$1, If[LessEqual[t$95$2, 1999999999999999996434887128370482831977857737518825000873086679459880803811809298994231532284537120019554351933503330752464420864], N[(120 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999995e123 or 2e129 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

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

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      6. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

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

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\color{blue}{\left(y - x\right)} \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      12. associate-/l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{60}{z - t}\right)\right)} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      16. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      17. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      18. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{-60}}{z - t} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      19. lower--.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \color{blue}{\left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      20. *-commutative N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{120 \cdot \left(\mathsf{neg}\left(a\right)\right)} \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120 \cdot a\right)\right)} \]

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

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      23. lower-*.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      24. metadata-eval 99.8%

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{-120} \cdot a \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{-60}{z - t} \cdot \left(y - x\right) - -120 \cdot a} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y - x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto -60 \cdot \frac{y - x}{z - \color{blue}{t}} \]

   6. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]

   7. Taylor expanded in z around inf

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

      2. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

   9. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]

   if -9.9999999999999995e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e129

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.2%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 56.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 100000000000000003441905430931245280917713770297417747470693647675065097962631447553892265814744827318497179085147422915077831721209019419643357959500300321574675254607872:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* 60 (- x y)) (- z t))))
  (if (<=
       t_1
       -4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336)
    (* -60 (/ y z))
    (if (<=
         t_1
         100000000000000003441905430931245280917713770297417747470693647675065097962631447553892265814744827318497179085147422915077831721209019419643357959500300321574675254607872)
      (* 120 a)
      (* 60 (/ x (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+144) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 1e+170) {
		tmp = 120.0 * a;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+144)) then
        tmp = (-60.0d0) * (y / z)
    else if (t_1 <= 1d+170) then
        tmp = 120.0d0 * a
    else
        tmp = 60.0d0 * (x / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+144) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 1e+170) {
		tmp = 120.0 * a;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+144:
		tmp = -60.0 * (y / z)
	elif t_1 <= 1e+170:
		tmp = 120.0 * a
	else:
		tmp = 60.0 * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+144)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (t_1 <= 1e+170)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+144)
		tmp = -60.0 * (y / z);
	elseif (t_1 <= 1e+170)
		tmp = 120.0 * a;
	else
		tmp = 60.0 * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336], N[(-60 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000000000000003441905430931245280917713770297417747470693647675065097962631447553892265814744827318497179085147422915077831721209019419643357959500300321574675254607872], N[(120 * a), $MachinePrecision], N[(60 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999999e144

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

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

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      6. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

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

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\color{blue}{\left(y - x\right)} \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      12. associate-/l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{60}{z - t}\right)\right)} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      16. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      17. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      18. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{-60}}{z - t} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      19. lower--.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \color{blue}{\left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      20. *-commutative N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{120 \cdot \left(\mathsf{neg}\left(a\right)\right)} \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120 \cdot a\right)\right)} \]

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

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      23. lower-*.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      24. metadata-eval 99.8%

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{-120} \cdot a \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{-60}{z - t} \cdot \left(y - x\right) - -120 \cdot a} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y - x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto -60 \cdot \frac{y - x}{z - \color{blue}{t}} \]

   6. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]

   7. Taylor expanded in z around inf

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

      2. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

   9. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]

   10. Taylor expanded in x around 0

       \[\leadsto -60 \cdot \frac{y}{z} \]
   11. Step-by-step derivation

   12. Applied rewrites 16.1%

       \[\leadsto -60 \cdot \frac{y}{z} \]

   if -4.9999999999999999e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e170

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.2%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 1e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. frac-2neg N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} \]

      5. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right) + \left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} \]

      6. mult-flip N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right) + \left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)}} \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right) + \left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right)\right)} \]

      8. +-commutative N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) + \left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)} \]

      9. add-flip N/A

         \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)\right) - \left(\mathsf{neg}\left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)\right) - \left(\mathsf{neg}\left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)\right) - \left(\mathsf{neg}\left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60} - \left(\mathsf{neg}\left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60 - \left(\mathsf{neg}\left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\color{blue}{\left(y - x\right)} \cdot 60 - \left(\mathsf{neg}\left(\left(a \cdot 120\right) \cdot \left(\mathsf{neg}\left(\left(z - t\right)\right)\right)\right)\right)\right) \]

      15. distribute-rgt-neg-out N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(y - x\right) \cdot 60 - \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\left(a \cdot 120\right) \cdot \left(z - t\right)\right)\right)}\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(y - x\right) \cdot 60 - \color{blue}{\left(a \cdot 120\right) \cdot \left(z - t\right)}\right) \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(y - x\right) \cdot 60 - \color{blue}{\left(a \cdot 120\right)} \cdot \left(z - t\right)\right) \]

      18. associate-*l* N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(y - x\right) \cdot 60 - \color{blue}{a \cdot \left(120 \cdot \left(z - t\right)\right)}\right) \]

      19. *-commutative N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(\left(y - x\right) \cdot 60 - \color{blue}{\left(120 \cdot \left(z - t\right)\right) \cdot a}\right) \]

   3. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - t}\right), \left(y - x\right), 60, \left(120 \cdot \left(z - t\right)\right), a\right)} \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 26.2%

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   6. Applied rewrites 26.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     (/ (* 60 (- x y)) (- z t))
     -4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336)
  (* -60 (/ y z))
  (* 120 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((60.0 * (x - y)) / (z - t)) <= -5e+144) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = 120.0 * a;
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (((60.0d0 * (x - y)) / (z - t)) <= (-5d+144)) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((60.0 * (x - y)) / (z - t)) <= -5e+144) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((60.0 * (x - y)) / (z - t)) <= -5e+144:
		tmp = -60.0 * (y / z)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) <= -5e+144)
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((60.0 * (x - y)) / (z - t)) <= -5e+144)
		tmp = -60.0 * (y / z);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(60 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], -4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336], N[(-60 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(120 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999999e144

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

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

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      4. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      6. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{60 \cdot \left(x - y\right)}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{\left(x - y\right) \cdot 60}\right)}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

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

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      10. lift--.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\color{blue}{\left(y - x\right)} \cdot 60}{\mathsf{neg}\left(\left(z - t\right)\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      12. associate-/l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)}} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{60}{\mathsf{neg}\left(\left(z - t\right)\right)} \cdot \left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{60}{z - t}\right)\right)} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      16. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      17. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(60\right)}{z - t}} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      18. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{-60}}{z - t} \cdot \left(y - x\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      19. lower--.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \color{blue}{\left(y - x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot 120 \]

      20. *-commutative N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{120 \cdot \left(\mathsf{neg}\left(a\right)\right)} \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120 \cdot a\right)\right)} \]

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

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      23. lower-*.f64 N/A

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{\left(\mathsf{neg}\left(120\right)\right) \cdot a} \]

      24. metadata-eval 99.8%

          \[\leadsto \frac{-60}{z - t} \cdot \left(y - x\right) - \color{blue}{-120} \cdot a \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{-60}{z - t} \cdot \left(y - x\right) - -120 \cdot a} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \color{blue}{\frac{y - x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z} - t} \]

      4. lower--.f64 50.2%

         \[\leadsto -60 \cdot \frac{y - x}{z - \color{blue}{t}} \]

   6. Applied rewrites 50.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z - t}} \]

   7. Taylor expanded in z around inf

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

      2. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{y - x}{z} \]

   9. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \frac{y - x}{\color{blue}{z}} \]

   10. Taylor expanded in x around 0

       \[\leadsto -60 \cdot \frac{y}{z} \]
   11. Step-by-step derivation

   12. Applied rewrites 16.1%

       \[\leadsto -60 \cdot \frac{y}{z} \]

   if -4.9999999999999999e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.2%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 51.2% accurate, 5.2× speedup

Math

\[120 \cdot a \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (* 120 a))

C

double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

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, a)
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), intent (in) :: a
    code = 120.0d0 * a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

Python

def code(x, y, z, t, a):
	return 120.0 * a

Julia

function code(x, y, z, t, a)
	return Float64(120.0 * a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 120.0 * a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(120 * a), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
3. Step-by-step derivation

   1. lower-*.f64 51.2%

      \[\leadsto 120 \cdot \color{blue}{a} \]

4. Applied rewrites 51.2%

   \[\leadsto \color{blue}{120 \cdot a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64
  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))