Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.7 → 6.9

Time: 27.1s

Precision: binary64

Cost: 1608

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z} + x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+154)
   (+ t (/ (- a y) (/ z (- t x))))
   (if (<= z 1.36e+191)
     (+ (* t (/ (- y z) (- a z))) (* x (+ 1.0 (/ (- z y) (- a z)))))
     (+ t (* x (/ (- y a) z))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+154) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= 1.36e+191) {
		tmp = (t * ((y - z) / (a - z))) + (x * (1.0 + ((z - y) / (a - z))));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y, z, t, a)
    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 (z <= (-1d+154)) then
        tmp = t + ((a - y) / (z / (t - x)))
    else if (z <= 1.36d+191) then
        tmp = (t * ((y - z) / (a - z))) + (x * (1.0d0 + ((z - y) / (a - z))))
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+154) {
		tmp = t + ((a - y) / (z / (t - x)));
	} else if (z <= 1.36e+191) {
		tmp = (t * ((y - z) / (a - z))) + (x * (1.0 + ((z - y) / (a - z))));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+154:
		tmp = t + ((a - y) / (z / (t - x)))
	elif z <= 1.36e+191:
		tmp = (t * ((y - z) / (a - z))) + (x * (1.0 + ((z - y) / (a - z))))
	else:
		tmp = t + (x * ((y - a) / z))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+154)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	elseif (z <= 1.36e+191)
		tmp = Float64(Float64(t * Float64(Float64(y - z) / Float64(a - z))) + Float64(x * Float64(1.0 + Float64(Float64(z - y) / Float64(a - z)))));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+154)
		tmp = t + ((a - y) / (z / (t - x)));
	elseif (z <= 1.36e+191)
		tmp = (t * ((y - z) / (a - z))) + (x * (1.0 + ((z - y) / (a - z))));
	else
		tmp = t + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+154], N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e+191], N[(N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(1.0 + N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000004e154

   1. Initial program 26.8

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

   2. Simplified 22.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      Proof
      (fma.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) x)): 5 points increase in error, 4 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 94 points increase in error, 23 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y z) (-.f64 t x))) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x): 38 points increase in error, 95 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 25.0

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

   4. Simplified 10.1

      \[\leadsto \color{blue}{t + \frac{-1 \cdot \left(y - a\right)}{\frac{z}{t - x}}} \]
      Proof
      (+.f64 t (/.f64 (*.f64 -1 (-.f64 y a)) (/.f64 z (-.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 y) (*.f64 -1 a))) (/.f64 z (-.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z))): 43 points increase in error, 18 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z) t)): 0 points increase in error, 0 points decrease in error

   if -1.00000000000000004e154 < z < 1.36e191

   1. Initial program 10.2

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

   2. Taylor expanded in x around -inf 9.3

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

   3. Simplified 5.9

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z} - x \cdot \left(\frac{y - z}{a - z} + -1\right)} \]
      Proof
      (-.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))) (*.f64 x (+.f64 (/.f64 (-.f64 y z) (-.f64 a z)) -1))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z))) (*.f64 x (+.f64 (/.f64 (-.f64 y z) (-.f64 a z)) -1))): 60 points increase in error, 13 points decrease in error
      (-.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)) (*.f64 x (+.f64 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) -1))): 0 points increase in error, 1 points decrease in error
      (-.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)) (*.f64 x (+.f64 (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))) (Rewrite<= metadata-eval (neg.f64 1))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)) (*.f64 x (Rewrite<= sub-neg_binary64 (-.f64 (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))) 1)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)) (*.f64 x (Rewrite<= associate--r+_binary64 (-.f64 (/.f64 y (-.f64 a z)) (+.f64 (/.f64 z (-.f64 a z)) 1))))): 1 points increase in error, 18 points decrease in error
      (-.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)) (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (/.f64 y (-.f64 a z)) (+.f64 (/.f64 z (-.f64 a z)) 1)) x))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)) (neg.f64 (*.f64 (-.f64 (/.f64 y (-.f64 a z)) (+.f64 (/.f64 z (-.f64 a z)) 1)) x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (-.f64 (/.f64 y (-.f64 a z)) (+.f64 (/.f64 z (-.f64 a z)) 1)) x)))): 0 points increase in error, 0 points decrease in error

   if 1.36e191 < z

   1. Initial program 28.7

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

   2. Simplified 23.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      Proof
      (fma.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) x)): 5 points increase in error, 4 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 94 points increase in error, 23 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y z) (-.f64 t x))) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x): 38 points increase in error, 95 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 24.2

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

   4. Simplified 7.2

      \[\leadsto \color{blue}{t - \frac{y - a}{z} \cdot \left(t - x\right)} \]
      Proof
      (-.f64 t (*.f64 (/.f64 (-.f64 y a) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 y a) (/.f64 z (-.f64 t x))))): 22 points increase in error, 33 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 y a) (-.f64 t x)) z))): 43 points increase in error, 18 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 t (neg.f64 (/.f64 (*.f64 (-.f64 y a) (-.f64 t x)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (*.f64 (-.f64 y a) (-.f64 t x))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (-.f64 y a) (-.f64 t x)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 -1 (-.f64 y a)) (-.f64 t x))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (*.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 y) (*.f64 -1 a))) (-.f64 t x)) z)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z) t)): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in t around 0 18.0

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

   6. Simplified 9.5

      \[\leadsto t - \color{blue}{\frac{y - a}{z} \cdot \left(-x\right)} \]
      Proof
      (*.f64 (/.f64 (-.f64 y a) z) (neg.f64 x)): 0 points increase in error, 0 points decrease in error
      (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (/.f64 (-.f64 y a) z) x))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (*.f64 (/.f64 (-.f64 y a) z) x))): 0 points increase in error, 0 points decrease in error
      (*.f64 -1 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y a) x) z))): 44 points increase in error, 49 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 6.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z} + x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	31.3
Cost	1568

\[\begin{array}{l} t_1 := \frac{z}{a - z} \cdot \left(-t\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-280}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.92 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 2
Error	18.8
Cost	1496

\[\begin{array}{l} t_1 := \frac{y - a}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+139}:\\ \;\;\;\;t + x \cdot t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-73}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 0.0028:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+30}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + t_1 \cdot \left(x - t\right)\\ \end{array} \]

Alternative 3
Error	18.7
Cost	1496

\[\begin{array}{l} t_1 := \frac{y - a}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+138}:\\ \;\;\;\;t + x \cdot t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-113}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 16500:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + t_1 \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4
Error	37.7
Cost	1372

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+144}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+65}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-182}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5
Error	36.6
Cost	1372

\[\begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+145}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+65}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-182}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6
Error	36.5
Cost	1372

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+145}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+68}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-255}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	36.4
Cost	1372

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+144}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+67}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-253}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-182}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	25.5
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -2.95 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -14000000:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9
Error	21.3
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+153}:\\ \;\;\;\;t - \frac{y}{t_2}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-114}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+32}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{t_2}\\ \end{array} \]

Alternative 10
Error	18.4
Cost	1364

\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+148}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1120000:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 11
Error	31.3
Cost	1240

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.55 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-193}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.92 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	31.3
Cost	1240

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-193}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.92 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	31.4
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-183}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.92 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-26}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 14
Error	20.8
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-96}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.92 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-20}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	19.9
Cost	1236

\[\begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 0.09:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	17.4
Cost	1232

\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ t_2 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 28:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	17.4
Cost	1232

\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-20}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 12.2:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 18
Error	29.7
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+146}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+66}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{+41}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	25.4
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -14500000:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 20
Error	10.0
Cost	1096

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+141}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+76}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 21
Error	29.1
Cost	1040

\[\begin{array}{l} t_1 := \frac{z}{a - z} \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	37.1
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+146}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+67}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23
Error	22.4
Cost	972

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-105}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 24
Error	20.2
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-159}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 25
Error	35.7
Cost	592

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+66}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 26
Error	36.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -15500000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 27
Error	45.4
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))